Results 201 to 210 of about 7,276 (215)

Robustly expansive homoclinic classes

Ergodic Theory and Dynamical Systems, 2004
From authors' summary: ``Let \(f: M\to M\) be a diffeomorphism defined in a three-dimensional compact boundary-less manifold \(M\). We prove that for an open dense set, \(C^1\)-robustly expansive homoclinic classes \(H(p)\) for \(f\) are hyperbolic. A diffeomorphism \(f\) is \(\alpha\)-expansive on a compact invariant set \(K\) if there is \(\alpha> 0\)
Pacifico, M. J., Pujals, E. R., Vieitez, J. L.   +2 more
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Periodically Expansive Homoclinic Classes

Journal of Dynamics and Differential Equations, 2012
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On bi-Lyapunov stable homoclinic classes

Bulletin of the Brazilian Mathematical Society, New Series, 2013
\textit{S. Smale}'s spectral decomposition theorem [Bull. Am. Math. Soc. 73, 747--817 (1967; Zbl 0202.55202)] gives a complete description of the structure of Axiom A diffeomorphisms. It is conjectured that some of the features of Smale's theorem hold generically for some general diffeomorphisms.
Arbieto, A., Carvalho, B., Cordeiro, W., Obata, D. J.   +3 more
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The Multidimensional Lorenz Attractor is a Homoclinic Class

Qualitative Theory of Dynamical Systems, 2014
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Bautista, S., Rojas, J. D.
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Stably average shadowable homoclinic classes

Nonlinear Analysis: Theory, Methods & Applications, 2011
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Generic diffeomorphisms with measure-expansive homoclinic classes

Journal of Difference Equations and Applications, 2013
We prove that for C1 generic diffeomorphisms, every measure-expansive locally maximal homoclinic class is hyperbolic.
Namjip Koo, Keonhee Lee, Manseob Lee
openaire   +1 more source

Bi-Lyapunov Stable Homoclinic Classes for C1 Generic Flows

Acta Mathematica Sinica, English Series, 2021
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The Rovella attractor is a homoclinic class

Bulletin of the Brazilian Mathematical Society, New Series, 2006
Rovella proved the existence of measure-persistent attractors for flows exhibiting a unique singularity with three real eigenvalues satisfying λ2 < λ3 < 0 < λ1 < −λ3 ([Ro]). In this paper we prove that most of them are in fact homoclinic classes.
Roger J. Metzger*, Carlos A. Morales**
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Expansive homoclinic classes of generic C 1-vector fields

Acta Mathematica Sinica, English Series, 2016
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Lee, Seunghee, Park, Junmi
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Robustly expansive codimension-one homoclinic classes are hyperbolic

Ergodic Theory and Dynamical Systems, 2009
AbstractWe shall prove thatC1-robustly expansive codimension-one homoclinic classes are hyperbolic.
Pacifico, M. J., Pujals, E. R., Sambarino, M., Vieitez, J. L.   +3 more
openaire   +2 more sources