Julia sets for Fibonacci endomorphisms of (2)

Author(s)

Bonnot, S. ^[1] ; de Carvalho, A. ^[1] ; Messaoudi, A. ^[2]

Affiliation

^[1] Univ Sao Paulo, Inst Matemat & Estat, Dept Matemat, Sao Paulo - Brazil

^[2] Univ Estadual Paulista, Dept Matemat Aplicada, Sao Jose Do Rio Preto - Brazil

• Document type: Journal article
• Source: DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL; v. 33, n. 4, p. 622-645, 2018.
• Web of Science Citations: 1

Abstract

We study the dynamics of the family f(c)(x, y)= (xy + c, x) of endomorphisms of , where c is a real parameter. We investigate several topological properties of the forward and backward filled Julia sets. Then, through the study of adapted dynamical filtrations of the plane, we prove that for the interval of parameters given by 0 < c <, these two filled Julia sets can be described explicitly as finite unions of invariant manifolds. (AU)

• FAPESP's process: 11/12650-4 - Topological models in holomorphic dynamics
• Grantee: Sylvain Philippe Pierre Bonnot
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 11/16265-8 - Low dimensional dynamics
• Grantee: Edson Vargas
• Support Opportunities: Research Projects - Thematic Grants