Blenders for a non-normally Henon-like family

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Shin Kiriki
Masaki Nakajima

Abstract

A blender is an indispensable concept presented by Bonatti and Diaz [3] to study high-dimensional $C^1$-robust transitive dynamics around heterodimensional cycles. In this paper, we present a certain Henon-like family of real quadratic diffeomorphisms on $\mathbb{R}^3$, which exhibits an phase transition from non-normal horseshoes to blenders. It can be observable from a rapidly jump of topological dimension for some projected stable segments in some characteristic region of $\mathbb{R}^3$.

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How to Cite
Kiriki, S., & Nakajima, M. (2010). Blenders for a non-normally Henon-like family. Tamkang Journal of Mathematics, 41(2), 149–166. https://doi.org/10.5556/j.tkjm.41.2010.666
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Papers
Author Biographies

Shin Kiriki

Department of Mathematics, Kyoto University of Education, Fukakusa-Fujinomori 1, Fushimi, Kyoto, 612-8522, Japan.

Masaki Nakajima

Odessey Co. Ltd., Kasumigaseki 3-2-5, Chiyoda, Tokyo, 100-6017, Japan.