Growth of number of periodic orbits of one family of skew product maps. Issue 1 (2nd January 2018)

• Record Type: Journal Article
• Authors: Esteves, Salete
• Is Part Of: Dynamical systems. Volume 33:Issue 1(2018)
• Page Start: 10
• Page End: 26
• Publication Date: 2018-01-02
• Subjects: Skew-product maps -- Artin-Mazur maps -- heterodimensional cycle -- homoclinic class -- index of a saddle; 37C20 -- 37C25 -- 37C29; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2017.1290051
• Languages: English
• ISSNs: 1468-9367

Abstract

ABSTRACT: In this article we introduce a one-parameter family of skew product ( G t ) t ∈ [−ε, ε] maps exhibiting a heterodimensional cycle such that the number of isolated periodic orbits inside it has not super-exponential growth. The dynamics in the central direction of the maps G t is described by a one-parameter family of system of iterated functions.