The nature of manifolds of periodic points for higher dimensional integrable maps

2005/08/31 by Satoru Saito, Saito, Satoru, Noriko Saitoh +1
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.math-ph/0508063

openalex publication_date 2005/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By studying periodic points for rational maps on \bmC^d with p invariants, we show that they form an invariant variety of dimension p if the periodicity conditions are `fully correlated', and a set of isolated points if the conditions are `uncorrelated'. We present many examples of the invariant varieties in the case of integrable maps. Moreover we prove that an invariant variety and a set of isolated points do not exist in one map simultaneously.

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