Vladimir Arnold

Vladimir Arnold
Vladimir Arnold in 2008
Vladimir Arnold 2008. godine
Datum rođenja12 jun 1937(1937-06-12)
Mesto rođenjaOdesa, Ukrajiniska SSR
 Sovjetski Savez
Datum smrti3. jun 2010.(2010-06-03) (72 god.)
Mesto smrtiPariz
 Francuska
PrebivališteSovjetski Savez
Državljanstvorusko
UniverzitetMoskovski državni univerzitet Lomonosov
DelovanjeMatematika

Vladimir Igorevič Arnold (alternativno spelovanje Arnoljd, rus. Влади́мир И́горевич Арно́льд, 12. jun 1937 – 3. jun 2010)[1][2][3] bio je sovijetski i ruski matematičar. Iako je najpoznatiji po Kolmogorov–Arnold–Moser teoremi o stabilnosti integrabilnih sistema, on je dao važan doprinos u nekoliko oblasti, uključujući teoriju dinamičkih sistema, algebru, teoriju katastrofe, topologiju, algebarsku geometriju, simplektičku geometriju, diferencijalne jednačine, klasičnu mehaniku, hidrodinamiku i teoriju singularnosti, uključujući postavljanje problema ADE klasifikacije, od svog prvog glavnog rezultata - rešenja Hilbertovog trinaestog problema 1957. u uzrastu od 19 godina. On je osnovao dve nove grane matematike - Kam teoriju i topološku teoriju Galoisa (ovo, sa njegovim učenikom Askoldom Hovanskijem).

Arnold je bio poznat i kao popularizator matematike. Kroz svoja predavanja, seminare i kao autor nekoliko udžbenika (poput poznatih Matematičkih metoda klasične mehanike) i popularnih knjiga iz polja matematike, uticao je na mnoge matematičare i fizičare.[4][5] Mnoge od njegovih knjiga su prevedene na engleski jezik. Njegovi pogledi na obrazovanje bili su izrazito anti-Burbaki.

Biografija

Vladimir Igorevič Arnold je rođen 12. juna 1937. godine u Odesi, Sovjetski Savez. Njegov otac bio je Igor Vladimirovič Arnold (1900–1948), matematičar. Njegova majka bila je Nina Alekandrovna Arnold (1909–1986, rođena Isakovič), jevrejska istoričarka umetnosti.[2] Kada je Arnoldu bilo trinaest godina, njegov ujak koji je bio inženjer upoznao ga je sa kalkulusom i pokazao mu kako se to može koristiti za razumevanje niza fizičkih pojava. To je doprinelo podsticanju njegovog interesovanja za matematiku i on je počeo samostalno da proučava matematičke knjige koje su mu ostale od njegovog oca, što je obuhvatalo dela Leonarda Ojlera i Šarla Ermita.[6]

Dok je bio student Andreja Kolmogorova na Moskovskom državnom univerzitetu i još uvek tinejdžer, Arnold je 1957. godine pokazao da se bilo koja kontinuirana funkcija više promenljivih može konstruisati sa konačnim brojem funkcija s dve promenljive, rešavajući tako Hilbertov trinaesti problem.[7] To je Kolmogorov–Arnoldova reprezentaciona teorema.

Izabrana bibliografija

  • 1966: Arnold, Vladimir (1966). „Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits”. Annales de l'Institut Fourier. 16: 319—361. doi:10.5802/aif.233. 
  • 1980: Mathematical Methods of Classical Mechanics, Springer-Verlag, ISBN 0-387-96890-3.[8][9]
  • 1985: (with S. M. Gusein-Zade & A. N. Varchenko) Singularities of Differentiable Maps, Volume I: The Classification of Critical Points, Caustics and Wave Fronts. Birkhäuser.
  • 1988: (with S. M. Gusein-Zade & A. N. Varchenko) Singularities of Differentiable Maps, Volume II: Monodromy and Asymptotics of Integrals. Monographs in Mathematics. Birkhäuser.
  • 1988: Geometrical Methods In The Theory Of Ordinary Differential Equations, Springer-Verlag ISBN 0-387-96649-8.
  • 1978; Ordinary Differential Equations, The MIT Press ISBN 0-262-51018-9.
  • 1989: (with A. Avez) Ergodic Problems of Classical Mechanics, Addison-Wesley ISBN 0-201-09406-1.
  • 1990: 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.[10][11][12]
  • 1995:Topological Invariants of Plane Curves and Caustics,[13] American Mathematical Society (1994) ISBN 978-0-8218-0308-0
  • 1999: (with Valentin Afraimovich) Bifurcation Theory And Catastrophe Theory Springer ISBN 3-540-65379-1
  • 1998: "On the teaching of mathematics" (Russian) Uspekhi Mat. Nauk 53 (1998), no. 1(319), 229–234; translation in Russian Math. Surveys 53(1): 229–236.
  • 2004: Teoriya Katastrof (Catastrophe Theory,[14] in Russian), 4th ed. Moscow, Editorial-URSS (2004), ISBN 5-354-00674-0.
  • 2001: "Tsepniye Drobi" (Continued Fractions, in Russian), Moscow (2001).
  • 2007; Yesterday and Long Ago, Springer (2007), ISBN 978-3-540-28734-6.
  • 2004: Vladimir I. Arnold, ур. (15. 11. 2004). Arnold's Problems (2nd изд.). Springer-Verlag. ISBN 978-3-540-20748-1. 
  • 2014: V. I. Arnold (2014). Mathematical Understanding of Nature: Essays on Amazing Physical Phenomena and Their Understanding by Mathematicians. American Mathematical Society. ISBN 978-1-4704-1701-7. 
  • Real Algebraic Geometry.
  • Lectures on Partial Differential Equations.[15][16]
  • 2015: Experimental Mathematics. American Mathematical Society (translated from Russian, 2015).
  • 2015: Lectures and Problems: A Gift to Young Mathematicians, American Math Society, (translated from Russian, 2015)
  • Arnolʹd, Vladimir Igorevich (1991). The Theory of Singularities and Its Applications (на језику: енглески). Cambridge University Press. ISBN 9780521422802. 

Sabrana dela

  • 2009: A. B. Givental; B. A. Khesin; J. E. Marsden; A. N. Varchenko; V. A. Vassilev; O. Ya. Viro; V. M. Zakalyukin (editors). Collected Works, Volume I: Representations of Functions, Celestial Mechanics, and KAM Theory (1957–1965). Springer
  • 2013: A. B. Givental; B. A. Khesin; A. N. Varchenko; V. A. Vassilev; O. Ya. Viro; (editors). Collected Works, Volume II: Hydrodynamics, Bifurcation Theory, and Algebraic Geometry (1965–1972). Springer.
  • 2016: Givental, A.B., Khesin, B., Sevryuk, M.B., Vassiliev, V.A., Viro, O.Y. (Eds.). Collected Works, Volume III: Singularity Theory 1972–1979. Springer.
  • 2018: Givental, A.B., Khesin, B., Sevryuk, M.B., Vassiliev, V.A., Viro, O.Y. (Eds.). Collected Works, Volume IV: Singularities in Symplectic and Contact Geometry 1980–1985. Springer.

Reference

  1. ^ Mort d'un grand mathématicien russe, AFP (Le Figaro)
  2. ^ а б Gusein-Zade, Sabir M.; Varchenko, Alexander N (decembar 2010), „Obituary: Vladimir Arnold (12 June 1937 – 3 June 2010)” (PDF), Newsletter of the European Mathematical Society, 78: 28—29 
  3. ^ Khesin, Boris; Tabachnikov, Sergei (2018). „Vladimir Igorevich Arnold. 12 June 1937 – 3 June 2010”. Biographical Memoirs of Fellows of the Royal Society. 64: 7—26. ISSN 0080-4606. doi:10.1098/rsbm.2017.0016 Слободан приступ. 
  4. ^ O'Connor, John J.; Robertson, Edmund F. „Vladimir Arnold”. MacTutor History of Mathematics archive. University of St Andrews. 
  5. ^ Bartocci, Claudio; Betti, Renato; Guerraggio, Angelo; Lucchetti, Roberto; Williams, Kim (2010). Mathematical Lives: Protagonists of the Twentieth Century From Hilbert to Wiles (на језику: енглески). Springer. стр. 211. ISBN 9783642136061. 
  6. ^ Табачников, С. Л. . "Интервью с В.И.Арнольдом", Квант, 1990, Nº 7, pp. 2–7. (in Russian)
  7. ^ Daniel Robertz (13. 10. 2014). Formal Algorithmic Elimination for PDEs. Springer. стр. 192. ISBN 978-3-319-11445-3. 
  8. ^ Review by Ian N. Sneddon (Bulletin of the American Mathematical Society, Vol. 2): http://www.ams.org/journals/bull/1980-02-02/S0273-0979-1980-14755-2/S0273-0979-1980-14755-2.pdf
  9. ^ Review by R. Broucke (Celestial Mechanics, Vol. 28): Bibcode:1982CeMec..28..345A.
  10. ^ Kazarinoff, N. (1. 9. 1991). „Huygens and Barrow, Newton and Hooke: Pioneers in Mathematical Analysis and Catastrophe Theory from Evolvents to Quasicrystals (V. I. Arnol'd)”. SIAM Review. 33 (3): 493—495. ISSN 0036-1445. doi:10.1137/1033119. 
  11. ^ Thiele, R. (1. 1. 1993). „Arnol'd, V. I., Huygens and Barrow, Newton and Hooke. Pioneers in Mathematical Analysis and Catastrophe Theory from Evolvents to Quasicrystals. Basel etc., Birkhäuser Verlag 1990. 118 pp., sfr 24.00. ISBN 3-7643-2383-3”. Journal of Applied Mathematics and Mechanics. 73 (1): 34. Bibcode:1993ZaMM...73S..34T. ISSN 1521-4001. doi:10.1002/zamm.19930730109. 
  12. ^ Heggie, Douglas C. (1. 6. 1991). „V. I. Arnol'd, Huygens and Barrow, Newton and Hooke, translated by E. J. F. Primrose (Birkhäuser Verlag, Basel 1990), 118 pp., 3 7643 2383 3, sFr 24.”. Proceedings of the Edinburgh Mathematical Society. Series 2. 34 (2): 335—336. ISSN 1464-3839. doi:10.1017/S0013091500007240 Слободан приступ. 
  13. ^ Goryunov, V. V. (1. 10. 1996). „V. I. Arnold Topological invariants of plane curves and caustics (University Lecture Series, Vol. 5, American Mathematical Society, Providence, RI, 1995), 60pp., paperback, 0 8218 0308 5, £17.50.”. Proceedings of the Edinburgh Mathematical Society. Series 2. 39 (3): 590—591. ISSN 1464-3839. doi:10.1017/S0013091500023348 Слободан приступ. 
  14. ^ Bernfeld, Stephen R. (1. 1. 1985). „Review of Catastrophe Theory”. SIAM Review. 27 (1): 90—91. JSTOR 2031497. doi:10.1137/1027019. 
  15. ^ Guenther, Ronald B.; Thomann, Enrique A. (2005). Renardy, Michael; Rogers, Robert C.; Arnold, Vladimir I., ур. „Featured Review: Two New Books on Partial Differential Equations”. SIAM Review. 47 (1): 165—168. ISSN 0036-1445. JSTOR 20453608. 
  16. ^ Groves, M. (2005). „Book Review: Vladimir I. Arnold, Lectures on Partial Differential Equations. Universitext”. ZAMM – Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik. 85 (4): 304. Bibcode:2005ZaMM...85..304G. ISSN 1521-4001. doi:10.1002/zamm.200590023. 

Literatura

  • Khesin, Boris; Tabachnikov, Serge (Coordinating Editors). "Tribute to Vladimir Arnold", Notices of the American Mathematical Society, March 2012, Volume 59, Number 3, pp. 378–399.
  • Khesin, Boris; Tabachnikov, Serge (Coordinating Editors). "Memories of Vladimir Arnold", Notices of the American Mathematical Society, April 2012, Volume 59, Number 4, pp. 482–502.
  • Boris A. Khesin; Serge L. Tabachnikov (2014). Arnold: Swimming Against the Tide. American Mathematical Society. ISBN 978-1-4704-1699-7. 
  • Leonid Polterovich; Inna Scherbak (7. 9. 2011). „V.I. Arnold (1937–2010)”. Jahresbericht der Deutschen Mathematiker-Vereinigung. 113 (4): 185—219. S2CID 122052411. doi:10.1365/s13291-011-0027-6. 
  • „Features: "Knotted Vortex Lines and Vortex Tubes in Stationary Fluid Flows"; "On Delusive Nodal Sets of Free Oscillations"” (PDF). EMS Newsletter (96): 26—48. jun 2015. ISSN 1027-488X. 

Spoljašnje veze

Vladimir Arnold на Викимедијиној остави.
  • V. I. Arnold's web page
  • Personal web page
  • V. I. Arnold lecturing on Continued Fractions
  • A short curriculum vitae
  • On Teaching Mathematics Архивирано на сајту Wayback Machine (28. април 2017), text of a talk espousing Arnold's opinions on mathematical instruction
  • Problems from 5 to 15, a text by Arnold for school students, available at the IMAGINARY platform
  • Vladimir Arnold на сајту MGP (језик: енглески)
  • S. Kutateladze, Arnold Is Gone
  • В.Б.Демидовичем (2009), МЕХМАТЯНЕ ВСПОМИНАЮТ 2: В.И.Арнольд, pp. 25–58
  • Author profile in the database zbMATH
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