Results 51 to 60 of about 864 (203)
Structurally stable homoclinic classes
Discrete and Continuous Dynamical Systems, 2016 arXiv admin note: substantial text overlap with arXiv:1410 ...
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Historic behavior in nonhyperbolic homoclinic classes
Proceedings of the American Mathematical Society, 2019 We show that C 1 C^1 -generically for ...
Barrientos, Pablo G. +4 more
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Abstract and Applied Analysis, 2014 We investigate a class of nonperiodic fourth order differential equations with general potentials. By using variational methods and genus properties in critical point theory, we obtain that such equations possess infinitely homoclinic solutions.
Liu Yang
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Homoclinic classes for sectional-hyperbolic sets [PDF]
Kyoto Journal of Mathematics, 2016 We prove that every sectional-hyperbolic Lyapunov stable set contains a nontrivial homoclinic class.
Arbieto, Alexander +2 more
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Homoclinics for singular strong force Lagrangian systems
Advances in Nonlinear Analysis, 2019 We study the existence of homoclinic solutions for a class of Lagrangian systems ddt$\begin{array}{} \frac{d}{dt} \end{array} $(∇Φ(u̇(t))) + ∇uV(t, u(t)) = 0, where t ∈ ℝ, Φ : ℝ2 → [0, ∞) is a G-function in the sense of Trudinger, V : ℝ × (ℝ2 ∖ {ξ}) → ℝ ...
Izydorek Marek +2 more
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Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT We develop a unified mathematical framework extending classical moment theory from discrete integer orders to a continuous spectrum of real orders f>0$$ f>0 $$, providing a systematic statistical characterization of complex systems exhibiting power‐law behavior.
Farrukh A. Chishtie
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Lyapunov stable homoclinic classes for smooth vector fields
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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Homoclinic Solutions for a Class of Hamiltonian Systems
Advanced Nonlinear Studies, 2004 Abstract We consider the first order Hamiltonian system q̇ = Hp(p, q), ṗ = −Hq(p, q), (HS) where p, q : ℝ → ℝ N (N ≥ 3), H ∈ C 1 (ℝ N × ℝ
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Mathematical Methods in the Applied Sciences, Volume 49, Issue 9, Page 9814-9831, June 2026.ABSTRACT Nonlinear differential equations play a fundamental role in modeling complex physical phenomena across solid‐state physics, hydrodynamics, plasma physics, nonlinear optics, and biological systems. This study focuses on the Shynaray II‐A equation, a relatively less‐explored parametric nonlinear partial differential equation that describes ...
Aamir Farooq +4 more
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Center Manifolds for Homoclinic Solutions
, 2000 In this article, center-manifold theory is developed for homoclinic solutions of ordinary differential equations or semilinear parabolic equations. A center manifold along a homoclinic solution is a locally invariant manifold containing all solutions ...
Sandstede, Björn
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