Existence of homoclinic orbits for unbounded time-dependent $p$-Laplacian systems
Electronic Journal of Qualitative Theory of Differential Equations, 2016 In this paper, we consider the following ordinary $p$-Laplacian system \begin{equation} \frac{d}{dt}\big(|\dot u(t)|^{p-2}\dot u(t)\big)-\nabla K(t,u(t)) + \nabla W(t,u(t))=f(t),\tag{$HS$} \end{equation} where $t\in \mathbb{R}$ and $ p>1$.
Adel Daouas
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Random Wandering Around Homoclinic-like Manifolds in Symplectic Map Chain
, 2001 We present a method to construct a symplecticity preserving renormalization group map of a chain of weakly nonlinear symplectic maps and obtain a general reduced symplectic map describing its long-time behaviour.
Goto, Shin-itiro +2 more
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A Note on the Existence of a Smale Horseshoe in the Planar Circular Restricted Three-Body Problem
Abstract and Applied Analysis, 2015 It has been proved that, in the classical planar circular restricted three-body problem, the degenerate saddle point processes transverse homoclinic orbits.
Xuhua Cheng, Zhikun She
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The point charge oscillator: qualitative and analytical investigations
Mathematical Modelling and Analysis, 2019 We study the mathematical model of the point charge oscillator which has been derived by A. Beléndez et al. [2]. First we determine the global phase portrait of this model in the Poincaré disk.
Klaus R. Schneider
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Partial Hyperbolicity and Homoclinic Tangencies [PDF]
, 2011 We show that any diffeomorphism of a compact manifold can be C1 approximated by diffeomorphisms exhibiting a homoclinic tangency or by diffeomorphisms having a partial hyperbolic ...
Crovisier, Sylvain +2 more
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Perturbed Li–Yorke homoclinic chaos
Electronic Journal of Qualitative Theory of Differential Equations, 2018 It is rigorously proved that a Li–Yorke chaotic perturbation of a system with a homoclinic orbit creates chaos along each periodic trajectory. The structure of the chaos is investigated, and the existence of infinitely many almost periodic orbits out of ...
Marat Akhmet +3 more
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Homoclinic and Heteroclinic Neural ODEs: Theory and Its Use to Construct New Chaotic Attractors
Journal of Optimization, Differential Equations and Their ApplicationsNew types of neural ordinary differential equations (NODE) with power nonlinearities are considered. For these NODE systems, new conditions for the existence of homoclinic and heteroclinic orbits are found.
Vasiliy Ye. Belozyorov +2 more
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Homoclinic orbits at infinity for second-order Hamiltonian systems with fixed energy
Electronic Journal of Differential Equations, 2015 We obtain the existence of homoclinic orbits at infinity for a class of second-order Hamiltonian systems with fixed energy. We use the limit for a sequence of approximate solutions which are obtained by variational methods.
Dong-Lun Wu, Shiqing Zhang
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Author’s reply to: Comments on “Asymptotically stable equilibrium points in new chaotic systems”
Nova Scientia, 2017 Since theorem 1 of (Elhadj and Sprott, 2012) is incorrect, some of the systems found in the article (Casas-García et al. 2016) may have homoclinic or heteroclinic orbits and may seem chaos in the Shilnikov sense.
K. Casas-García +4 more
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Infinitely many homoclinic orbits for Hamiltonian systems with group symmetries
Electronic Journal of Differential Equations, 1999 This paper deals via variational methods with the existence of infinitely many homoclinic orbits for a class of the first-order time-dependent Hamiltonian systems $$ dot{z}=JH_z(t,z) $$ without any periodicity assumption on $H$, providing that $H(t,z ...
Cheng Lee
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