Hyperbolicity of renormalization for dissipative gap mappings
-
Published:2021-09-03
Issue:
Volume:
Page:1-42
-
ISSN:0143-3857
-
Container-title:Ergodic Theory and Dynamical Systems
-
language:en
-
Short-container-title:Ergod. Th. Dynam. Sys.
Author:
CLARK TREVOR,GOUVEIA MÁRCIO
Abstract
Abstract
A gap mapping is a discontinuous interval mapping with two strictly increasing branches that have a gap between their ranges. They are one-dimensional dynamical systems, which arise in the study of certain higher dimensional flows, for example the Lorenz flow and the Cherry flow. In this paper, we prove hyperbolicity of renormalization acting on
$C^3$
dissipative gap mappings, and show that the topological conjugacy classes of infinitely renormalizable gap mappings are
$C^1$
manifolds.
Funder
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
FP7 Ideas: European Research Council
Fundação de Amparo à Pesquisa do Estado de São Paulo
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics