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Homoclinic chaos and energy condition violation [PDF]
, 2006 In this letter we discuss the connection between so-called homoclinic chaos and the violation of energy conditions in locally rotationally symmetric Bianchi type IX models, where the matter is assumed to be non-tilted dust and a positive cosmological ...
A. Rendall +8 more
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Stabilizing a homoclinic stripe [PDF]
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2018 For a large class of reaction–diffusion systems with large diffusivity ratio, it is well known that a two-dimensional stripe (whose cross-section is a one-dimensional homoclinic spike) is unstable and breaks up into spots. Here, we study two effects that can stabilize such a homoclinic stripe. First, we consider the addition of anisotropy to the model.
Theodore Kolokolnikov +3 more
openaire +2 more sources
Proceedings of the American Mathematical Society, 1976 Results of R. C. Robinson and D. Pixton on the existence of homoclinic points for diffeomorphisms on the two-sphere are extended. An application to area preserving diffeomorphisms on surfaces is given.
openaire +2 more sources
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
core +1 more source
Novel Hyperbolic Homoclinic Solutions of the Helmholtz-Duffing Oscillators
Shock and Vibration, 2016 The exact and explicit homoclinic solution of the undamped Helmholtz-Duffing oscillator is derived by a presented hyperbolic function balance procedure.
Yang-Yang Chen +2 more
doaj +1 more source
, 2017 Floer theory was originally devised to estimate the number of 1-periodic orbits of Hamiltonian systems. In earlier works, we constructed Floer homology for homoclinic orbits on two dimensional manifolds using combinatorial techniques.
Hohloch, Sonja
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Bifurcation of Nongeneric Homoclinic Orbit Accompanied by Pitchfork Bifurcation
Abstract and Applied Analysis, 2014 The bifurcation of a nongeneric homoclinic orbit (i.e., the orbit comes from the equilibrium along the unstable manifold instead of the center manifold) connecting a nonhyperbolic equilibrium is investigated, and the nonhyperbolic equilibrium undergoes ...
Fengjie Geng, Song Li
doaj +1 more source
Resonant Homoclinic Flips Bifurcation in Principal Eigendirections
Abstract and Applied Analysis, 2013 A codimension-4 homoclinic bifurcation with one orbit flip and one inclination flip at principal eigenvalue direction resonance is considered. By introducing a local active coordinate system in some small neighborhood of homoclinic orbit, we get the ...
Tiansi Zhang, Xiaoxin Huang, Deming Zhu
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Continuum-wise expansive homoclinic classes for robust dynamical systems
Advances in Difference Equations, 2019 In the study, we consider continuum-wise expansiveness for the homoclinic class of a kind of C1 $C^{1}$-robustly expansive dynamical system. First, we show that if the homoclinic class H(p,f) $H(p, f)$, which contains a hyperbolic periodic point p, is R ...
Manseob Lee
doaj +1 more source
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
doaj +1 more source