Filled Julia set of some class of Hénon-like maps. Issue 1 (2nd January 2020)

• Record Type: Journal Article
• Authors: Antonio Caprio, Danilo
• Is Part Of: Dynamical systems. Volume 35:Issue 1(2020)
• Page Start: 156
• Page End: 183
• Publication Date: 2020-01-02
• Subjects: Holomorphic dynamics -- stable manifolds -- filled Julia sets; 37F45 -- 37F50; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2019.1663790
• Languages: English
• ISSNs: 1468-9367

Abstract

ABSTRACT: In this work we consider a class of endomorphisms of R 2 defined by f ( x, y ) = ( x y + c, x ), where c ∈ R is a real number and we prove that when − 1 < c < 0, the forward filled Julia set of f is the union of stable manifolds of fixed and 3 − periodic points of f . We also prove that the backward filled Julia set of f is the union of unstable manifolds of the saddle fixed and 3 − periodic points of f .