منابع مشابه
Abundance of C-robust homoclinic tangencies
A diffeomorphism f has a C-robust homoclinic tangency if there is a C-neighbourhood U of f such that every diffeomorphism in g ∈ U has a hyperbolic set Λg, depending continuously on g, such that the stable and unstable manifolds of Λg have some non-transverse intersection. For every manifold of dimension greater than or equal to three, we exhibit a local mechanism (blender-horseshoes) generatin...
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In this paper, we propose a rigorous computational method for detecting homoclinic tangencies and structurally unstable connecting orbits. It is a combination of several tools and algorithms, including the interval arithmetic, the subdivision algorithm, the Conley index theory, and the computational homology theory. As an example we prove the existence of generic homoclinic tangencies in the Hé...
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The maximum number of non-overlapping unit spheres in R that can simultaneously touch another unit sphere is given by the kissing number, k(3) = 12. Here, we present a proof that the maximum number of tangencies in any kissing configuration is 24 and that, up to isomorphism, there are only two configurations for which this maximum is achieved. The result is motivated by a three-dimensional crys...
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The problem of understanding the dynamical behavior of diffeomorphisms has played a central role in the field of dynamical systems. One way of approaching this question is to ask about generic behavior in the space of diffeomorphisms. Another way to approach it is to ask about behavior in some specific parametrized family. The family of diffeomorphisms of R introduced by Hénon has often played ...
متن کاملHomoclinic Tangencies, Ω-Moduli, and Bifurcations
|A survey of author's results related to the problems of existence of continuous invariants (moduli) of-conjugacy of multidimensional diieomorphisms with homoclinic tan-gencies is presented. The problem of bifurcations of periodic orbits is considered in the case of four-dimensional diieomorphisms with a nontransversal homoclinic orbit to a xed point of saddle{focus type. INTRODUCTION It is wel...
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2012
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/25/12/3277