---
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.'
address:
- 'Trevor Clark, Imperial College London, London, UK'
- 'Márcio Gouveia, IBILCE-UNESP, CEP 15054-000, S. J. Rio Preto, São Paulo, Brazil'
author:
- Trevor Clark
- Márcio Gouveia
bibliography:
- 'biblio.bib'
title: Hyperbolicity of renormalization for dissipative gap mappings
---

Introduction
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Preliminaries
=============

Renormalization of decomposed mappings {#sec:decomp}
======================================

The derivative of the renormalization operator {#sec:derivative}
==============================================

Manifold structure of the conjugacy classes
===========================================

Acknowledgements {#acknowledgements .unnumbered}
================

The authors would like to Liviana Palmisano for some helpful comments about @MP. They also thank Sebastian van Strien for his encouragement and several helpful conversations.

{'source': 'arXiv_out/1907'}