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Value Distribution and Growth of Solutions of Certain Painlevé Equations

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Dynamical Systems in Theoretical Perspective (DSTA 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 248))

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Abstract

As a result of classification of second order ordinary differential equations without movable branch points, a number of the so-called Painlevé equations was obtained. Among them, six irreducible equations are the best known. They led to the recognition of new functions, called the Painlevé transcendents. The Painlevé equations have numerous applications in modern mathematics and mathematical physics. The solutions of these equations, as they are meromorphic in the complex plane can be studied from the perspective of value distribution and growth theory, with such values as defect, deviation or multiplicity index estimated.

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, University of Szczecin, ul. Wielkopolska 15, 70-451, Szczecin, Poland

    Ewa Ciechanowicz

  2. Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland

    Galina Filipuk

Authors
  1. Ewa Ciechanowicz
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  2. Galina Filipuk
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Correspondence to Ewa Ciechanowicz .

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Editors and Affiliations

  1. Department of Automation, Biomechanics and Mechatronics, Łódź University of Technology, Łódź, Poland

    Jan Awrejcewicz

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Ciechanowicz, E., Filipuk, G. (2018). Value Distribution and Growth of Solutions of Certain Painlevé Equations. In: Awrejcewicz, J. (eds) Dynamical Systems in Theoretical Perspective. DSTA 2017. Springer Proceedings in Mathematics & Statistics, vol 248. Springer, Cham. https://doi.org/10.1007/978-3-319-96598-7_9

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