Homoclinic orbits for a class of Hamiltonian systems
Differential and Integral Equations, 1992 The Hamiltonian system under consideration is governed by equations of the form \[ \ddot q+V_ q(t,q)=\ddot q-L(t)q+W_ q(t,q)=0, \] where \(L(t)\) is a positive definite matrix and further technical conditions, among other things, ensure that the origin is a local maximum of \(V\) for all \(t\).
Omana, W., Willem, M.
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Nonexistence of Homoclinic Solutions for a Class of Discrete Hamiltonian Systems
Abstract and Applied Analysis, 2013 We give several sufficient conditions under which the first-order nonlinear discrete Hamiltonian system Δx(n)=α(n)x(n+1)+β(n)|y(n)|μ-2y(n),Δy(n)=-γ(n)|x(n+1)|ν-2x(n+1)-α(n)y(n) has no solution (x(n),y(n)) satisfying condition ...
Xiaoping Wang
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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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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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Measure expansive homoclinic classes for generic diffeomorphisms
Applied Mathematical Sciences, 2015 Let f : M ! M be a dieomorphism on a closed smooth n(n 2)dimensional Riemannian manifold M. For C 1 generic f; if a homoclinic class Hf (p) is measure expansive then it is hyperbolic.
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Homoclinic orbits for a class of symmetric Hamiltonian systems
Electronic Journal of Differential Equations, 1994 of Hamiltonian systems that are symmetric with respect to independent variable (time). For the scalar case we prove existence and uniqueness of a positive homoclinic solution. For the system case we prove existence of symmetric homoclinic orbits.
Philip Korman, Alan C. Lazer
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On homoclinic orbits for a class of damped vibration systems [PDF]
, 2012 Juntao Sun +2 more
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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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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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Partial hyperbolicity far from homoclinic bifurcations
, 2008 We prove that any diffeomorphism of a compact manifold can be C^1-approximated by a diffeomorphism which exhibits a homoclinic bifurcation (a homoclinic tangency or a heterodimensional cycle) or by a diffeomorphism which is partially hyperbolic (its ...
Crovisier, Sylvain
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