Results 21 to 30 of about 7,276 (215)
HYPERBOLICITY OF HOMOCLINIC CLASSES OF VECTOR FIELDS [PDF]
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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Homoclinic orbits for a class of $p$-Laplacian systems with periodic assumption
Electronic Journal of Qualitative Theory of Differential Equations, 2013 In this paper, by using a linking theorem, some new existence criteria of homoclinic orbits are obtained for the $p$-Laplacian system $d(|\dot{u}(t)|^{p-2}\dot{u}(t))/dt+\nabla V(t,x)=f(t)$, where $p>1$, $V(t,x)=-K(t,x)+W(t,x)$.
Xingyong Zhang
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Electronic Journal of Qualitative Theory of Differential Equations, 2021 We obtain an existence theorem of nonzero solution for a class of bounded selfadjoint operator equations. The main result contains as a special case the existence result of a nontrivial homoclinic orbit of a class of Hamiltonian systems by Coti Zelati ...
Mingliang Song, Runzhen Li
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Topics in Cognitive Science, EarlyView., 2023 Abstract Fractal fluctuations are a core concept for inquiries into human behavior and cognition from a dynamic systems perspective. Here, we present a generalized variance method for multivariate detrended fluctuation analysis (mvDFA). The advantage of this extension is that it can be applied to multivariate time series and considers intercorrelation ...
Sebastian Wallot +5 more
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Expansive homoclinic classes [PDF]
Nonlinearity, 2009 We prove that for $C^1$ generic diffeomorphisms, every expansive homoclinic class is hyperbolic.
Yang, Dawei, Gan, Shaobo
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Mathematics, 2022 The mean curvature problem is an important class of problems in mathematics and physics. We consider the existence of homoclinic solutions to a discrete partial mean curvature problem, which is tied to the existence of discrete solitons.
Yanshan Chen, Zhan Zhou
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Homoclinic solutions for a class of second-order Hamiltonian systems with locally defined potentials
Electronic Journal of Differential Equations, 2017 In this article, we establish sufficient conditions for the existence of homoclinic solutions for a class of second-order Hamiltonian systems $$ \ddot u(t)-L(t)u(t)+\nabla W\bigl(t,u(t)\bigr)=f(t), $$ where L(t) is a positive definite symmetric ...
Xiang Lv
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Homoclinic classes with shadowing [PDF]
Journal of Inequalities and Applications, 2012 Abstract We show that for C 1 generic diffeomorphisms, an isolated homoclinic class is shadow-able if and only if it is a hyperbolic basic set. Mathematics Subject Classification 2000: 37C20; 37C05; 37C29; 37D05.
Ahn, Jiweon, Lee, Keonhee, Lee, Manseob
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Mixing-like properties for some generic and robust dynamics [PDF]
, 2014 We show that the set of Bernoulli measures of an isolated topologically mixing homoclinic class of a generic diffeomorphism is a dense subset of the set of invariant measures supported on the class.
Arbieto, Alexander +2 more
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Frontiers in Physics, 2022 A class of generalized homoclinic solutions of the nonlinear Schrödinger (NLS) equation in 1+1 dimensions is studied. These are homoclinic breathers that are shown to be derivable from the ratio of Riemann theta functions for the genus-2 solutions of ...
Alfred R. Osborne
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