On the existence of homoclinic solutions of a class of discrete nonlinear periodic systems
, 2010 In this paper, we obtain a new sufficient condition on the existence of homoclinic solutions of a class of discrete nonlinear periodic systems by using critical point theory in combination with periodic approximations.
Yu, Jianshe, Zhou, Zhan
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Homoclinic solutions in periodic partial difference equations
Advances in Nonlinear AnalysisBy using critical point theory in combination with periodic approximations, we obtain novel sufficient conditions for the existence of nontrivial homoclinic solutions for a class of periodic partial difference equations with sign-changing mixed ...
Mei Peng, Zhou Zhan, Yu Jianshe
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The Plykin and Solenoid attractor are homoclinic classes
Revista Colombiana de MatemáticasA homoclinic class is the closure of the transverse intersection points of the stable and unstable manifolds of a hyperbolic periodic orbit. In this paper, we prove, using the techniques presented in [1], that the Plykin and the Solenoid attractors are a homoclinic class.
Raibel Arias Cantillo +1 more
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Sufficient conditions for a partially hyperbolic attractor to be a homoclinic class
, 2010 We prove that a partially hyperbolic attractor with two-dimensional central direction Λ is a homoclinic class if it exhibits a hyperbolic periodic orbit O and a Lorenz-like singularity σ with Wu(σ)∩Ws(O)≠∅ such that Ws(σ) is dense in ...
Morales, C.A., C.A. Morales
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Homoclinic Solutions for a Class of Second Order Nonautonomous Singular Hamiltonian Systems
Abstract and Applied Analysis, 2014 We are concerned with the existence of homoclinic solutions for the following second order nonautonomous singular Hamiltonian systems u¨+atWuu=0, (HS) where -∞
Ziheng Zhang +2 more
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Multiplicity Of Homoclinic Orbits In Quasi-Linear Autonomous Lagrangian Systems
The existence of at least two homoclinic orbits is proved by A. Ambrosetti and V. Coti Zelati (Multiple homoclinic orbits for a class of conservative systems, Rend. Sem. Mat. Univ.
Buffoni, Boris, Landry, Laurent
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Analytical study of the Lorenz system: Existence of infinitely many periodic orbits and their topological characterization. [PDF]
Proc Natl Acad Sci U S A, 2023 Pinsky T.
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Multiplicity of homoclinic orbits in quasi-linear autonomous Lagrangian systems [PDF]
, 2020 The existence of at least two homoclinic orbits is proved by A. Ambrosetti and V. Coti Zelati (Multiple homoclinic orbits for a class of conservative systems, Rend. Sem. Mat. Univ.
B Buffoni, L Landry
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Temperature elevations can induce switches to homoclinic action potentials that alter neural encoding and synchronization. [PDF]
Nat Commun, 2022 Hesse J +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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