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Hyperbolicity of the complex of free factors
Hyperbolicity of the complex free factors Group Theory
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2011/9/13
Abstract: We prove that the complex of free factors of a free group of finite rank is hyperbolic.
Hyperbolicity of the invariant sets for the real polynomial maps
Cantor set Complex dynamic Hyperbolic Logistic map Polynomial map
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2011/2/25
It is well known that for a > 4, the dynamical behaviors of the logistic map fa(x) = ax(1 − x) on the maximal invariant compact set are “simple”, which could be clearly explained by the theories...
Essential hyperbolicity and homoclinic bifurcations: a dichotomy phenomenon/mechanism for diffeomorphisms
Essential hyperbolicity homoclinic bifurcations dichotomy phenomenon/mechanism for diffeomorphisms
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2010/11/22
We prove that any diffeomorphism of a compact manifold can be approximated in topology C1 by another diffeomorphism exhibiting a homoclinic bifurcation (a homoclinic tangency or a heterodimensional c...