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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
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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

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