Essential hyperbolicity and homoclinic bifurcations: a dichotomy phenomenon-mechanism for diffeomorphisms - Mathematics > Dynamical SystemsReport as inadecuate




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Abstract: We prove that any diffeomorphism of a compact manifold can be approximated intopology C1 by another diffeomorphism exhibiting a homoclinic bifurcation ahomoclinic tangency or a heterodimensional cycle or by one which isessentially hyperbolic it has a finite number of transitive hyperbolicattractors with open and dense basin of attraction.



Author: Sylvain Crovisier, Enrique R. Pujals

Source: https://arxiv.org/







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