Results 11 to 20 of about 7,276 (215)
On the F-expanding of Homoclinic class [PDF]
, 2017 We establish a closing property for thin trapped homoclinic classes. Taking advantage of this property, we proved that if the homoclinic class $H(p)$ admits a dominated splitting $T_{H(p)}M=E\oplus_{
Wanlou Wu, Bo Li
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Infinitely many homoclinic solutions for a class of nonlinear difference equations
Electronic Journal of Qualitative Theory of Differential Equations, 2012 By using the Symmetric Mountain Pass Theorem, we establish some existence criteria to guarantee a class of nonlinear difference equation has infinitely many homoclinic orbits. Our conditions on the nonlinear term are rather relaxed and we generalize some
Peng Chen, Zhengmei Wang
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Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this paper, we obtain the multiplicity of homoclinic solutions for a class of asymptotically autonomous Hamiltonian systems with indefinite sign potentials. The concentration-compactness principle is applied to show the compactness. As a byproduct, we
Dong-Lun Wu
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Structurally stable homoclinic classes
Discrete and Continuous Dynamical Systems, 2015 arXiv admin note: substantial text overlap with arXiv:1410 ...
Xiao Wen
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Homoclinic Orbits for a Class of Nonperiodic Hamiltonian Systems [PDF]
Abstract and Applied Analysis, 2012 We study the following nonperiodic Hamiltonian system ż=JHz(t,z), where H∈C1(R×R2N,R) is the form H(t,z)=(1/2)B(t)z⋅z+R(t,z). We introduce a new assumption on B(t) and prove that the corresponding Hamiltonian operator has only point spectrum.
Wenping Qin, Jian Zhang, Fukun Zhao
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On the hyperbolicity of homoclinic classes
Discrete & Continuous Dynamical Systems - A, 2009 We give a sufficient criterion for the hyperbolicity of a homoclinic class. More precisely, if the homoclinic class $H(p)$ admits a partially hyperbolic splitting $T_{H(p)}M=E^s\oplus_ ...
Christian Bonatti +3 more
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Lyapunov stable homoclinic classes for smooth vector fields [PDF]
Open Mathematics, 2019 In this paper, we show that for generic C1, if a flow Xt has the shadowing property on a bi-Lyapunov stable homoclinic class, then it does not contain any singularity and it is hyperbolic.
Lee Manseob
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Hyperbolic periodic points for chain hyperbolic homoclinic classes
Discrete and Continuous Dynamical Systems, 2015 In this paper we establish a closing property and a hyperbolic closing property for thin trapped chain hyperbolic homoclinic classes with one dimensional center in partial hyperbolicity setting.
Sun, Wenxiang, Yang, Yun
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On $C^1$-persistently expansive homoclinic classes
Discrete & Continuous Dynamical Systems - A, 2006 Let $f: M \to M$ be a diffeomorphism defined in a $d$-dimensional compact boundary-less manifold $M$. We prove that $C^1$-persistently expansive homoclinic classes $H(p)$, $p$ an $f$-hyperbolic periodic point, have a dominated splitting $E\oplus F$, $\dim(E)=\mbox{index}(p)$.
Martı́n Sambarino +3 more
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Existence of homoclinic orbits for a class of nonlinear functional difference equations
Electronic Journal of Differential Equations, 2016 By using critical point theory, we prove the existence of a nontrivial homoclinic orbit for a class of nonlinear functional difference equations. Our conditions on the nonlinear term do not need to satisfy the well-known global Ambrosetti-Rabinowitz ...
Xia Liu, Tao Zhou, Haiping Shi
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