Results 181 to 190 of about 864 (203)

Periodically Expansive Homoclinic Classes

Journal of Dynamics and Differential Equations, 2012
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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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Existence of Homoclinic Solutions for a Class of Damped Vibration Problems

Qualitative Theory of Dynamical Systems, 2022
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Huijuan Xu, Shan Jiang, Guanggang Liu
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Multibump homoclinic solutions for a class of second order, almost periodic Hamiltonian systems

Nonlinear Differential Equations and Applications, 1997
We prove the existence of infinitely many homoclinic solutions for a class of second order Hamiltonian systems in RN of the form −q ̈ = −q + α(t)W′(q) where α is almost periodic and W is ...
COTI ZELATI V, NOLASCO, MARGHERITA, MONTECCHIARI P   +2 more
exaly   +1 more source

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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Homoclinic orbits for a class of hemivariational inequalities

Applicable Analysis, 1995
Using a new compact imbedding theorem of C. De Coster and M.Willem [5], we prove the existence of homoclinic orbits for a class of hemivariational inequalities.
S. Adly, D. Goeleven
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HYPERBOLICITY OF HOMOCLINIC CLASSES OF VECTOR FIELDS

Journal of the Australian Mathematical Society, 2014
Let${\it\gamma}$be a hyperbolic closed orbit of a$C^{1}$vector field$X$on a compact$C^{\infty }$manifold$M$and let$H_{X}({\it\gamma})$be the homoclinic class of$X$containing${\it\gamma}$. In this paper, we prove that if a$C^{1}$-persistently expansive homoclinic class$H_{X}({\it\gamma})$has the shadowing property, then$H_{X}({\it\gamma})$is hyperbolic.
KEONHEE LEE, MANSEOB LEE, SEUNGHEE LEE
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On the existence of non-trivial homoclinic classes

Ergodic Theory and Dynamical Systems, 2007
AbstractWe show that, for C1-generic diffeomorphisms, every chain recurrent class C that has a partially hyperbolic splitting $E^s\oplus E^c\oplus E^u$ with dimEc=1 either is an isolated hyperbolic periodic orbit, or is accumulated by non-trivial homoclinic classes.
Bonatti, Christian, Gan, Shaobo, Wen, Lan   +2 more
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Multiple homoclinic orbits for a class of Hamiltonian systems

Calculus of Variations and Partial Differential Equations, 2001
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Homoclinic solutions for a class of fourth‐order difference equations

Mathematical Methods in the Applied Sciences, 2015
In this paper, a class of fourth‐order nonlinear difference equation is considered. By making use of the critical point theory, we establish various sets of sufficient conditions for the existence of homoclinic solutions and give some new results. One of our results generalizes and improves the results in the literature.
Shi, Haiping, Liu, Xia, Zhang, Yuanbiao
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