Regular and Chaotic Dynamics

, Volume 19, Issue 1, pp 1–19 | Cite as

Paul Painlevé and his contribution to science

  • Alexey V. Borisov
  • Nikolay A. Kudryashov


The life and career of the great French mathematician and politician Paul Painlevé is described. His contribution to the analytical theory of nonlinear differential equations was significant. The paper outlines the achievements of Paul Painlevé and his students in the investigation of an interesting class of nonlinear second-order equations and new equations defining a completely new class of special functions, now called the Painlevé transcendents. The contribution of Paul Painlevé to the study of algebraic nonintegrability of the N-body problem, his remarkable observations in mechanics, in particular, paradoxes arising in the dynamics of systems with friction, his attempt to create the axiomatics of mechanics and his contribution to gravitation theory are discussed.


mathematician politician Painlevé equations Painlevé transcendents Painlevé paradox 

MSC2010 numbers

01-00 01A55 01A60 


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© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.Institute of Computer ScienceUdmurt State UniversityIzhevskRussia
  2. 2.A.A. Blagonravov Mechanical Engineering Research Institute of RASMoscowRussia
  3. 3.Institute of Mathematics and Mechanics of the Ural Branch of RASEkaterinburgRussia
  4. 4.Department of Applied MathematicsNational Research Nuclear University “MEPhI”MoscowRussia

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