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Conservative homoclinic bifurcations and some applications
conservative dynamics homoclinic bifurcations Newhouse phenomena persistent tangencies Hausdorff dimension standard map three body problem Sitnikov problem
2015/9/25
We study generic unfoldings of homoclinic tangencies of two dimensional area preserving diffeomorphisms (conservative Newhouse phenomena) and show that they give rise to invariant hyperbolic sets of a...
Periodic windows distribution resulting from homoclinic bifurcations in the two-parameter space
Homoclinic systems Periodic windows Bifurcation
2010/12/28
Periodic solution parameters, in chaotic dynamical systems, form periodic windows with characteristic distribution in two-parameter spaces. Recently, general properties of this organization have been ...
Essential hyperbolicity and homoclinic bifurcations: a dichotomy phenomenon/mechanism for diffeomorphisms
Essential hyperbolicity homoclinic bifurcations dichotomy phenomenon/mechanism for diffeomorphisms
2010/11/22
We prove that any diffeomorphism of a compact manifold can be approximated in topology C1 by another diffeomorphism exhibiting a homoclinic bifurcation (a homoclinic tangency or a heterodimensional c...