scholarly journals On the Conjugation of Local Diffeomorphisms Infinitely Tangent to the Identity

Foliations ◽  
2018 ◽  
Author(s):  
Hiroko Kawabe
Keyword(s):  
Local Diffeomorphisms ◽  
Tangent To The Identity

scholarly journals Hadamard–Perron theorems and effective hyperbolicity

2014 ◽  
Vol 36 (1) ◽  
pp. 23-63 ◽  
Author(s):  
VAUGHN CLIMENHAGA ◽  
YAKOV PESIN
Keyword(s):  
Closing Lemma ◽  
Stable And Unstable Manifolds ◽  
Local Dynamics ◽  
Local Diffeomorphisms ◽  
Finite Amount ◽  
Amount Of Information ◽  
Unstable Manifolds

We prove several new versions of the Hadamard–Perron theorem, which relates infinitesimal dynamics to local dynamics for a sequence of local diffeomorphisms, and in particular establishes the existence of local stable and unstable manifolds. Our results imply the classical Hadamard–Perron theorem in both its uniform and non-uniform versions, but also apply much more generally. We introduce a notion of ‘effective hyperbolicity’ and show that if the rate of effective hyperbolicity is asymptotically positive, then the local manifolds are well behaved with positive asymptotic frequency. By applying effective hyperbolicity to finite-orbit segments, we prove a closing lemma whose conditions can be verified with a finite amount of information.

scholarly journals SRB measures for partially hyperbolic attractors of local diffeomorphisms

2018 ◽  
Vol 40 (6) ◽  
pp. 1545-1593
Author(s):  
ANDERSON CRUZ ◽  
PAULO VARANDAS
Keyword(s):  
Thermodynamic Formalism ◽  
Positive Lebesgue Measure ◽  
Stable Bundle ◽  
Local Diffeomorphism ◽  
Local Diffeomorphisms ◽  
Axiom A ◽  
Srb Measures ◽  
Cone Field ◽  
Hyperbolic Attractors ◽  
Partially Hyperbolic

We contribute to the thermodynamic formalism of partially hyperbolic attractors for local diffeomorphisms admitting an invariant stable bundle and a positively invariant cone field with non-uniform cone expansion at a positive Lebesgue measure set of points. These include the case of attractors for Axiom A endomorphisms and partially hyperbolic endomorphisms derived from Anosov. We prove these attractors have finitely many SRB measures, that these are hyperbolic, and that the SRB measure is unique provided the dynamics is transitive. Moreover, we show that the SRB measures are statistically stable (in the weak$^{\ast }$ topology) and that their entropy varies continuously with respect to the local diffeomorphism.

Summable formal invariant curves of diffeomorphisms

2011 ◽  
Vol 32 (1) ◽  
pp. 211-221 ◽  
Author(s):  
L. LÓPEZ-HERNANZ
Keyword(s):  
Power Series ◽  
Formal Power Series ◽  
Infinitesimal Generator ◽  
Invariant Curves ◽  
Tangent To The Identity ◽  
Formal Power

AbstractLet F be a tangent to the identity diffeomorphism in (ℂ2,0) and X its infinitesimal generator. We prove that Camacho and Sad’s formal invariant curves of X give summable formal power series, whose sums correspond to the parabolic curves found by Hakim for F and F−1.

scholarly journals Parabolic curves of diffeomorphisms asymptotic to formal invariant curves

2018 ◽  
Vol 2018 (739) ◽  
pp. 277-296 ◽  
Author(s):  
Lorena López-Hernanz ◽  
Fernando Sanz Sánchez
Keyword(s):  
Fixed Points ◽  
Invariant Curve ◽  
Invariant Curves ◽  
Parabolic Curve ◽  
Tangent To The Identity

AbstractWe prove that ifFis a tangent to the identity diffeomorphism at0\in\mathbb{C}^{2}and Γ is a formal invariant curve ofFwhich is not contained in the set of fixed points then there exists a parabolic curve (attracting or repelling) ofFasymptotic to Γ.

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