Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-27T05:35:32.732Z Has data issue: false hasContentIssue false
  • English
  • Français

Decay of geometry in the cubic family

Published online by Cambridge University Press:  01 October 1998

GRZEGORZ ŚWIATEK  and
EDSON VARGAS
GRZEGORZ ŚWIATEK
Affiliation:
Penn State University, 209 Mc Allister, University Park, PA 16802, USA
EDSON VARGAS
Affiliation:
IME-USP, Cx. P.: 66281 CEP: 05315-970, São Paulo, Brasil
Get access Rights & Permissions [Opens in a new window]

Abstract

We study the box geometry of bi-modal maps. As has been expected, unlike in the unimodal case, there may be non-renormalizable mappings which do not show the decay of geometry. We provide an example. On the other hand, we come up with a natural pattern in which the critical orbits are closely intertwined, but the decay of geometry persists. All this is done in the context of a generally defined box inducing construction for bi-modal maps.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 18 , Issue 5 , October 1998 , pp. 1311 - 1329
Copyright
© 1998 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)