Homoclinic class - Open Access .click

Applied Mathematics and Computation, 2013
Authos' abstract: We deal with the existence and multiplicity of homoclinic solutions of the following damped vibration problem \[ \ddot{u}(t) + q(t)\dot{u}(t) - L(t)u(t) + \nabla W(t, u(t)) = 0, \] where $L(t)$ and $W(t, x)$ are neither autonomous nor periodic in $t$. Our approach is variational and it is based on the critical point theory.
Xianhua Tang, Ravi P Agarwal
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The Multidimensional Lorenz Attractor is a Homoclinic Class

Qualitative Theory of Dynamical Systems, 2014
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Bautista, S., Rojas, J. D.
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Robustly expansive homoclinic classes

Ergodic Theory and Dynamical Systems, 2004
From authors' summary: ``Let $f: M\to M$ be a diffeomorphism defined in a three-dimensional compact boundary-less manifold $M$. We prove that for an open dense set, $C^1$-robustly expansive homoclinic classes $H(p)$ for $f$ are hyperbolic. A diffeomorphism $f$ is $\alpha$-expansive on a compact invariant set $K$ if there is $\alpha> 0$
Pacifico, M. J., Pujals, E. R., Vieitez, J. L. +2 more
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Generation of homoclinic tangencies by $C^1$-perturbations

Discrete and Continuous Dynamical Systems, 2010
International audienceGiven a [C^1] -diffeomorphism [f] of a compact manifold, we show that if the stable/unstable dominated splitting along a saddle is weak enough, then there is a small [C^1] -perturbation that preserves the orbit of the saddle and ...
Gourmelon, Nicolas
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mathematics
homoclinic solutions
dynamical systems math.ds

fos: mathematics
mathematics - dynamical systems
homoclinic solution

variational methods
analysis
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