Studies on spaces of initial conditions for nonautonomous mappings of the plane

2017/02/20 by Takafumi Mase, Mase, Takafumi · 3 citations
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1702.05884

openalex publication_date 2017/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study nonautonomous mappings of the plane by means of spaces of initial conditions. First we introduce the notion of a space of initial conditions for nonautonomous systems and we study the basic properties of general equations that have spaces of initial conditions. Then, we consider the minimization of spaces of initial conditions for nonautonomous systems and we show that if a nonautonomous mapping of the plane with a space of initial conditions, and unbounded degree growth, has zero algebraic entropy, then it must be one of the discrete Painlevé equations in the Sakai classification.

Cited by

• Commuting integrable maps from a deformed D₄ cluster algebra
• On the geometry of a 4-dimensional extension of a q-Painlevé I equation with symmetry type A₁⁽¹⁾
• Integrable deformations of cluster maps of type D_2N

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