Vladimir Arnold
Vladimir Arnold in 2008
Born	(1937-06-12)12 June 1937 Odessa, Soviet Union
Died	3 June 2010(2010-06-03) (aged 72) Paris, France
Nationality	Soviet Union Russian
Fields	Mathematics
Alma mater	Moscow State University
Doctoral advisor	Andrey Kolmogorov
Doctoral students	Alexander Givental Askold Khovanskii Boris Shapiro Alexander Varchenko
Known for	Arnold's cat map Arnold conjecture Arnold's rouble problem KAM theorem

Vladimir Igorevich Arnold (alternative spelling Arnol'd, Russian: Влади́мир И́горевич Арно́льд, 12 June 1937 – 3 June 2010^[1]) was a Soviet and Russian mathematician. While he is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable Hamiltonian systems, he made important contributions in several areas including dynamical systems theory, catastrophe theory, topology, algebraic geometry, classical mechanics and singularity theory, including posing the ADE classification problem, since his first main result—the partial solution of Hilbert's thirteenth problem in 1957 at the age of 19.

Biography[link]

While a student of Andrey Kolmogorov at Moscow State University and still a teenager, Arnold showed in 1957 that any continuous function of several variables can be constructed with a finite number of two-variable functions, thereby partially solving Hilbert's thirteenth problem.

After graduating from Moscow State University in 1959, he worked there until 1986 (a professor since 1965), and then at Steklov Mathematical Institute.

He became an academician of the Academy of Sciences of the Soviet Union (Russian Academy of Science since 1991) in 1990.^[2] Arnold can be said to have initiated the theory of symplectic topology as a distinct discipline. The Arnold conjecture on the number of fixed points of Hamiltonian symplectomorphisms and Lagrangian intersections were also a major motivation in the development of Floer homology.

Arnold worked at the Steklov Mathematical Institute in Moscow and at Paris Dauphine University up until his death. As of 2006^[update] he was reported to have the highest citation index among Russian scientists,^[3] and h-index of 40.

To his students and colleagues Arnold was known also for his sense of humour. For example, once at his seminar in Moscow, at the beginning of the school year, when he usually was formulating new problems, he said:

There is a general principle that a stupid man can ask such questions to which one hundred wise men would not be able to answer. In accordance with this principle I shall formulate some problems.

Arnold died of peritonitis on 3 June 2010 in Paris, nine days before his 73rd birthday.^[4] His students include Alexander Givental, Victor Vassiliev and Askold Khovanskii.

In a telegram to Arnold's family, Russian President Dmitry Medvedev stated:

“The death of Vladimir Arnold, one of the greatest mathematicians of our time, is an irretrievable loss for world science. It is difficult to overestimate the contribution made by academician Arnold to modern mathematics and the prestige of Russian science.

Teaching had a special place in Vladimir Arnold's life and he had great influence as an enlightened mentor who taught several generations of talented scientists.

The memory of Vladimir Arnold will forever remain in the hearts of his colleagues, friends and students, as well as everyone who knew and admired this brilliant man.”^[5]

Popular mathematical writings[link]

Arnold is well known for his lucid writing style, combining mathematical rigour with physical intuition, and an easy conversational style of teaching. His writings present a fresh, often geometric approach to traditional mathematical topics like ordinary differential equations, and his many textbooks have proved influential in the development of new areas of mathematics. However, Arnold's books have been criticized for supporting the theory with statements meant to teach an intuitive understanding, without providing the tools necessary to prove these statements.^[6]

Arnold was an outspoken critic of the trend of high levels of abstraction in mathematics during the middle of the last century. He had very strong opinions on how this approach—which was most popularly implemented by the Bourbaki school in France—initially had a negative impact on French, and then later other countries', mathematical education.^[7][8] Arnold's sharp critique of Bourbaki approach was in turn criticized by other mathematicians.^[9]

Honours and awards[link]

• Lenin Prize (1965, with Andrey Kolmogorov)
• Crafoord Prize (1982, with Louis Nirenberg)
• Foreign Honorary Member of the American Academy of Arts and Sciences (1987)^[10]
• Harvey Prize (1994)
• Dannie Heineman Prize for Mathematical Physics (2001)
• Wolf Prize in Mathematics (2001)
• State Prize of the Russian Federation (2007)^[11]
• Shaw Prize in mathematical sciences (2008)

The minor planet 10031 Vladarnolda was named after him in 1981 by Lyudmila Georgievna Karachkina.

Selected bibliography[link]

• V. I. Arnold, Mathematical Methods of Classical Mechanics, Springer-Verlag (1989), ISBN 0-387-96890-3.
• V. I. Arnold, Geometrical Methods In The Theory Of Ordinary Differential Equations, Springer-Verlag (1988), ISBN 0-387-96649-8.
• V. I. Arnold, Ordinary Differential Equations, The MIT Press (1978), ISBN 0-262-51018-9.
• V. I. Arnold, A. Avez, Ergodic Problems of Classical Mechanics, Addison-Wesley (1989), ISBN 0-201-09406-1.
• V.I. Arnold, Huygens and Barrow, Newton and Hooke: Pioneers in mathematical analysis and catastrophe theory from evolvents to quasicrystals, Eric J.F. Primrose translator, Birkhäuser Verlag (1990) ISBN 3-7643-2383-3 .
• V. I. Arnold, Teoriya Katastrof (Catastrophe Theory, in Russian), 4th ed. Moscow, Editorial-URSS (2004), ISBN 5-354-00674-0.
• V. I. Arnold, "Tsepniye Drobi" (Continued Fractions, in Russian), Moscow (2001).
• V. I. Arnold, Yesterday and Long Ago, Springer (2007), ISBN 978-3-540-28734-6.
• Arnold, V. I.; V. S. Afraimovich (1999). Bifurcation Theory And Catastrophe Theory. Springer. ISBN 3-540-65379-1. 
• Arnolʹd, V. I.: On the teaching of mathematics. (Russian) Uspekhi Mat. Nauk 53 (1998), no. 1(319), 229—234; translation in Russian Math. Surveys 53 (1998), no. 1, 229—236.
• Vladimir I. Arnold, ed. (2004). Arnold's Problems (2nd ed.). Springer-Verlag. ISBN 3-540-20748-1. 

See also[link]

Mathematics portal

• Arnold's cat map
• Arnold conjecture
• Arnold's rouble problem
• KAM theorem
• Gömböc

References[link]

External links[link]

Wikimedia Commons has media related to: Vladimir Arnold

• V. I. Arnold's web page
• Personal web page
• V. I. Arnold lecturing on Continued Fractions
• A short curriculum vitae
• On Teaching Mathematics, text of a talk espousing Arnold's opinions on mathematical instruction
• Vladimir Arnold at the Mathematics Genealogy Project
• S. Kutateladze, Arnold Is Gone

Vladimir (English) Владимир (Russian)
-  City[citation needed]  -
View of Vladimir
Location of Vladimir Oblast in Russia
Vladimir Location of Vladimir in Vladimir Oblast
Coordinates: 56°09′N 40°25′E / 56.15°N 40.417°E / 56.15; 40.417Coordinates: 56°09′N 40°25′E / 56.15°N 40.417°E / 56.15; 40.417
Coat of arms	Flag
City Day	The first Sunday of September[citation needed]
Administrative status (as of April 2011)
Country	Russia
Federal subject	Vladimir Oblast[1]
Administratively subordinated to	City of Vladimir[1]
Administrative center of	Vladimir Oblast[1]
Municipal status (as of August 2009)
Urban okrug	Vladimir Urban Okrug[2]
Administrative center of	Vladimir Urban Okrug[2]
Head[citation needed]	Sergey Sakharov[citation needed]
Representative body	Council of People's Deputies[citation needed]
Statistics
Area	308 km2 (119 sq mi)[citation needed]
Population (2010 Census, preliminary)	345,598 inhabitants[3]
- Rank in 2010	51st
Population (2002 Census)	315,954 inhabitants[4]
- Rank in 2002	58th
Density	1,122 /km2 (2,910 /sq mi)[5]
Time zone	MSK (UTC+04:00)[6]
Founded	990 or 1108(see text)
Dialing code(s)	+7 4922[citation needed]
Official website
Vladimir on WikiCommons

Vladimir (Russian: Влади́мир; IPA: [vlɐˈdʲimʲɪr]) is a city and the administrative center of Vladimir Oblast, Russia, located on the Klyazma River, 200 kilometers (120 mi) to the east of Moscow along the M7 motorway. Population: 345,598 (2010 Census preliminary results);^[3] 315,954 (2002 Census);^[4] 349,702 (1989 Census).^[7]

Vladimir was one of the medieval capitals of Russia, and two of its cathedrals are a World Heritage Site. It is served by the Semyazino Airport, and during the Cold War Vladimir was host to Dobrynskoye air base.

History[link]

Foundation date controversy[link]

Assumption Cathedral was a venerated model for cathedrals all over Russia

The area occupied by the city of Vladimir has been inhabited by humans (at least intermittently) for approximately 25,000 years (see Sungir). Traditionally, the founding date of Vladimir has been acknowledged as 1108, as the first mention of Vladimir in the Primary Chronicle appears under that year. This view attributes the founding of the city, and its name, to Vladimir Monomakh, who inherited the region as part of the Rostov-Suzdal Principality in 1093. In 1958, the 850th anniversary of the city foundation was celebrated, with many monuments from the celebrations adorning the city squares.

In the 1990s, a new opinion developed that the city is older than this. Scholars reinterpreted certain passages in the Hypatian Codex, which mentions that the region was visited by Vladimir the Great, the "father" of Russian Orthodoxy, in 990, so as to move the city foundation date to that year. The defenders of the previously uncontested founding year of 1108 dispute the claims of those who support the new date, arguing that the new theory was fabricated in order to provide a reason to have a celebration in 1995.

The neighboring town of Suzdal, for instance, was mentioned in 1024, and yet its 12th century inhabitants alluded to Vladimir as a young town and treated its rulers with arrogance. In the words of a major chronicle, they said that the people of Vladimir were "their kholops and scions". In the seniority conflicts of the 12th and early 13th centuries, Vladimir was repeatedly described as a "young town" compared to Suzdal and Rostov. The Charter of Vladimir, the basic law of the city passed in 2005, explicitly mentions 990 as the date of the city's foundation.^[8]

Golden Age[link]

St. Demetrius' Cathedral is famous for its masterfully carved exterior, representing the Biblical story of King David. The photo was taken in 1912.

Regardless of which founding date is most accurate, the city's most historically significant events occurred after the turn of the 12th century. Serving its original purpose as a defensive outpost for the Rostov-Suzdal principality, Vladimir had little political or military influence throughout the reign of Vladimir Monomakh (1113–1125), or his son Yury Dolgoruky ("long arms") (1154–1157).

It was only under Dolgoruky's son, Andrei Bogolyubsky (1157–1175), that it became the center of the Vladimir-Suzdal principality. Thus began the city's Golden Age, which lasted until the Mongol invasion of Russia in 1237. During this time Vladimir enjoyed immense growth and prosperity, and Andrei oversaw the building of the Golden Gates and the Cathedral of the Assumption. In 1164, Andrei even attempted to establish a new metropolitanate in Vladimir, separate from that of Kiev, but was rebuffed by the Patriarch of Constantinople.^[9]

Scores of Russian, German, and Georgian masons worked on Vladimir's white stone cathedrals, towers, and palaces. Unlike any other northern buildings, their exterior was elaborately carved with the high relief stone sculptures. Only three of these edifices stand today: the Assumption Cathedral, the Cathedral of Saint Demetrius, and the Golden Gate. During Andrei's reign, a royal palace in Bogolyubovo was built, as well as the world-famous Intercession Church on the Nerl, now considered one of the jewels of ancient Russian architecture. Andrei was assassinated at his palace at Bogolyubovo in 1175.

Decline[link]

The main church of the Princesses' Convent was built by Ivan III of Moscow to replace an old crumbling church where the consorts of the Vladimir-Suzdal monarchs had been buried

Vladimir was besieged by the Mongol-Tatar hordes under Batu Khan, and finally overrun on February 8, 1238. A great fire destroyed thirty-two limestone buildings on the first day alone, while the grand prince's family perished in a church where they sought refuge from the flames. The grand prince himself managed to escape, only to fall at the Battle of the Sit River the following month.

After the Mongols, Vladimir never fully recovered, and even though the most important Rus prince (usually the Prince of Moscow, but sometimes of Tver or another principality) was styled the Grand Prince of Vladimir, the title had become merely an honorific symbol of majesty. From 1299 to 1325, the city was seat of the metropolitans of Kiev and All Rus, until Metropolitan Peter moved the see to Moscow. The Grand Prince of Vladimir were originally crowned in Vladimir's Assumption Cathedral, but when Moscow superseded Vladimir as the seat of the Grand Prince, the Assumption Cathedral in the Moscow Kremlin, loosely copied by the Italian architect Aristotele Fioravanti from Vladimir's original, became the site where the grand princes were crowned. Even after the rise of Moscow though, Grand Princes of Moscow built several new churches in Vladimir, notably the Annunciation church at Snovitsy (ca. 1501), three kilometers north-west of the city, and a charming church in the Knyaginin nunnery (ca. 1505), with murals dating to 1648.

Remains of the prince-saint Alexander Nevsky were kept in the ancient Nativity abbey of Vladimir until 1703, when Peter the Great had them transferred to the Monastery (now Lavra) of Aleksandr Nevsky in St. Petersburg. The Nativity church itself (1191–1196) collapsed several years later, when an attempt was made to make more windows in its walls in an effort to brighten the interior.

Administrative and municipal status[link]

Administratively, along with seventeen rural localities, it is incorporated as the City of Vladimir—an administrative unit with the status equal to that of the districts.^[1] Municipally, the City of Vladimir is incorporated as Vladimir Urban Okrug.^[2]

Climate[link]

Vladimir experiences a humid continental climate (Köppen climate classification Dfb) with long, cold winters and short, warm summers.

Sightseeing[link]

Modern Vladimir is a part of the Golden ring of the ancient Russian cities and a significant tourist center. Its three chief monuments, White Monuments of Vladimir and Suzdal, inscribed by UNESCO on the World Heritage List, are the following:

1. The magnificent five-domed Assumption Cathedral was designed as a sepulcher of grand princes and dedicated to the holy icon Theotokos of Vladimir, which had been brought to the city by Andrew the Pious. The cathedral was constructed in 1158–1160, expanded in 1185–1189, and painted by the great Andrei Rublev and Daniil Chyorny in 1408. In 1810, they added a lofty bell-tower in Neoclassical style.
2. The warrior-like cathedral of St. Demetrius was built in 1194–1197 as a private chapel of Vsevolod the Big Nest in the courtyard of his palace and was consecrated to his holy patron, St. Demetrius. For all its formal unity, the cathedral represents a truly international project of Russian and Byzantine masters, Friedrich Barbarossa's masons, and carvers sent by Queen Tamar of Georgia.
3. The Golden Gate, originally a tower over the city's main gate, was built in 1158–1164. The gate acquired its present form after having been grossly reconstructed in the late 18th century, to prevent the dilapidated structure from tumbling down.

Other remarkable monuments of pre-Mongol Russian architecture are scattered in the vicinity. For more information on them, see Suzdal, Yuriev-Polsky, Bogolyubovo, and Kideksha.

Modern Vladimir[link]

Lenina Avenue in Vladimir

Economy[link]

Vladimir is home to several electrical and chemical factories, several food processing plants, two large thermal power stations, and the headquarters of the 27th Guards Missile Army of the Strategic Rocket Forces. Tourism related to the historical sites is a major contributor to the city economy.

Education[link]

Vladimir is home to the following education establishments:

• Vladimir State University
• Vladimir Judicial Institute of the Ministry of Justice
• Vladimir Business Institute
• The American Home English & Russian Language School

Vladimir is also home to the Federal Centre for Animal Health and Welfare.

Transport[link]

Vladimir is linked to Moscow and Nizhny Novgorod by railway and the M7 highway. Local transport includes buses, trolleybuses,fixed-route minivans, and taxis. Taxi and some minivan service is available 24 hours a day.

Sports[link]

The city association football team, FC Torpedo Vladimir, currently plays in the Football Championship of the National League (former Russian First Division), having entered the second level of Russian professional football after seventeen years of competing in Russian Second Division and Russian Third League. Vladimir VC (previously known as Skat and Dinamo Vladimir) represents the city in Volleyball Major League B – Zone Europe.

Vladimir is also home to Polaris-Vladimir ice hockey club, which competes in regional hockey competitions and Russian minor leagues, and both male and female Luch table-tennis teams.

International relations[link]

Twin towns and sister cities[link]

Vladimir is twinned with:^[11]

• Anghiari, Italy
• Baotze, China
• Bloomington-Normal, United States
• Campobasso, Italy
• Canterbury, United Kingdom
• Cebu, Philippines^[12]
• Chongqing, China
• Erlangen, Germany
• Kerava, Finland
• Kardzhali, Bulgaria
• Nara, Japan
• Sarasota, United States
• Trento, Italy
• Ústí nad Labem, Czech Republic
• Jelenia Góra, Poland

Notable people[link]

• Valentin Afonin, association football player
• Nikolai Andrianov, gymnast
• Vladimir Artemov, gymnast
• Aleksey Batalov, actor
• Mikhail Lazarev, admiral
• Yuri Levitan, radio announcer
• Alexey Prokurorov, cross-country skier
• Yuri Ryazanov, gymnast
• Vasily Shulgin, politician
• Mikhail Speransky, statesman
• Aleksandr Stoletov, physicist
• Nikolai Stoletov, general
• Sergei Taneyev, composer
• Dmitri Vyazmikin, association football player
• Denis Yevsikov, association football player
• Nikolay Zhukovsky, scientist
• Anna Loginova, fashion model

References[link]

Notes[link]

Sources[link]

• Законодательное Собрание Владимирской области. Закон №130-ОЗ от 10 декабря 2001 г. «Об административно-территориальном устройстве Владимирской области и о порядке его изменения», в ред. Закона №24-ОЗ от 27 апреля 2011 г «О внесении изменений в статьи 8, 9 Закона Владимирской области "Об административно-территориальном устройстве Владимирской области и о порядке его изменения"». Вступил в силу со дня официального опубликования (13 декабря 2001 г.). Опубликован: "Владимирские ведомости", №232, 13 декабря 2001 г. (Legislative Assembly of Vladimir Oblast. Law #130-OZ of December 10, 2001 On the Administrative-Territorial Structure of Vladimir Oblast and on Procedures for Its Change, as amended by the Law #24-OZ of April 27, 2011 On Amending Articles 8, 9 of the Law of Vladimir Oblast "On the Administrative-Territorial Structure of Vladimir Oblast and on Procedures for Its Change". Effective as of the day of the official publication (December 13, 2001).).
• Законодательное Собрание Владимирской области. Закон №189-ОЗ от 26 ноября 2004 г. «О наделении статусом городского округа муниципального образования город Владимир Владимирской области», в ред. Закона №108-ОЗ от 10 августа 2009 г «О внесении изменений в Закон Владимирской области "О наделении статусом городского округа муниципального образования город Владимир Владимирской области"». Вступил в силу со дня официального опубликования (1 декабря 2004 г.). Опубликован: "Владимирские ведомости", №333, 1 декабря 2004 г. (Legislative Assembly of Vladimir Oblast. Law #189-OZ of November 26, 2004 On Granting Urban Okrug Status to the Municipal Formation of the City of Vladimir of Vladimir Oblast, as amended by the Law #108-OZ of August 10, 2009 On Amending the Law of Vladimir Oblast "On Granting Urban Okrug Status to the Municipal Formation of the City of Vladimir of Vladimir Oblast". Effective as of the day of the official publication (December 1, 2004).).

Further reading[link]

• Craft Brumfield, William (2004). A History of Russian Architecture. Seattle: University of Washington Press. ISBN 978-0-295-98394-3. 

External links[link]

• Official website of Vladimir (Russian)
• Vladimir travel guide from Wikitravel
• Tourist information on Vladimir
• The American Home in Vladimir

v t e Cities and towns in Vladimir Oblast Administrative center: Vladimir Alexandrov Gorokhovets Gus-Khrustalny Kameshkovo Karabanovo Kirzhach Kolchugino Kosteryovo Kovrov Kurlovo Lakinsk Melenki Murom Petushki Pokrov Raduzhny Sobinka Strunino Sudogda Suzdal Vladimir Vyazniki Yuryev-Polsky

v t e Golden Ring of Russia Alexandrov Bogolyubovo Gorokhovets Gus-Khrustalny Ivanovo Kideksha Kostroma Moscow Palekh Pereslavl-Zalessky Plyos Rostov Sergiyev Posad Suzdal Tutayev Uglich Vladimir Yaroslavl Yuryev-Polsky