Indices of the iterates of R³-homeomorphisms at Lyapunov stable fixed points

2007/04/18 by Francisco R. Ruiz del Portal, del Portal, Francisco R. Ruiz, José Manuel Salazar +1
Engineering · Mathematics · #37B30 #37C25 #54H25 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations #math.DS #math.GT #msc:37B30 #msc:37C25 #msc:54H25

paper · pdf · doi:10.48550/arxiv.0704.2402

19 pages, 8 figures

arxiv created 2007/04/18 · openalex publication_date 2007/04/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given any positive sequence (\c_n\_n ∈ \Bbb N), we construct orientation preserving homeomorphisms (f:\Bbb R³ → \Bbb R³) such that (Fix(f)=Per(f)=\0\), (0) is Lyapunov stable and (\limsup (|i(f^m, 0)|)/(c_m)= ∞). We will use our results to discuss and to point out some strong differences with respect to the computation and behavior of the sequences of the indices of planar homeomorphisms.

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