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On critical point for two-dimensional holomorphic systems

Published online by Cambridge University Press:  12 May 2016

FRANCISCO VALENZUELA-HENRÍQUEZ
FRANCISCO VALENZUELA-HENRÍQUEZ*
Affiliation:
Instituto de Matemática, Pontificia Universidad Católica de Valparaíso, Blanco Viel 596, Cerro Barón, Valparaíso, Chile email francisco.valenzuela@pucv.cl, pancho.valenzuela.math@gmail.com
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Abstract

Let $f:M\rightarrow M$ be a biholomorphism on a two-dimensional complex manifold, and let $X\subseteq M$ be a compact $f$-invariant set such that $f|_{X}$ is asymptotically dissipative and without periodic sinks. We introduce a solely dynamical obstruction to dominated splitting, namely critical point. Critical point is a dynamical object and captures many of the dynamical properties of a one-dimensional critical point.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 37 , Issue 7 , October 2017 , pp. 2276 - 2312
Copyright
© Cambridge University Press, 2016 

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