Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-Uniformly Hyperbolic Horseshoes Arising from Bifurcations of
  Poincar\'e Heteroclinic Cycles   The purpose of this paper is to advance the knowledge of the dynamics arising
from the creation and subsequent bifurcation of Poincar\'e heteroclinic cycles.
The problem is central to dynamics: it has to be addressed if, for instance,
one aims at describing the typical orbit behaviour of a typical system, thus
providing a global scenario for the ensemble of dynamical systems - see the
Introduction and [P1, P2]. Here, we shall consider smooth, i.e. $C^\infty$,
one-parameter families of dissipative, meaning non-conservative, surface
diffeomorphisms. An hetereoclinic cycle may appear when the parameter evolves
and an orbit of tangency, say quadratic, is created between stable and unstable
manifolds (lines) of periodic orbits that belong to a basic hyperbolic set. The
key novelty is to allow this basic set, a horseshoe, to have Hausdorff
dimension bigger than one. In the present paper we do assume such a dimension
to be beyond one, but in a limited way, as explicitly indicated in the
Introduction. [A mild non-degeneracy condition on the family of maps is
assumed: at the orbit of tangency the invariant lines, stable and unstable,
cross each other with positive relative speed]. We then prove that most
diffeomorphisms, corresponding to parameter values near the bifurcating one,
are non-uniformly hyperbolic in a neighborhood of the horseshoe and the orbit
of tangency; such diffeomorphisms display no attractors nor repellors in such a
neighborhood. A first precise formulation of our main theorem is at the
Introduction and a more encompassing version at the end of the paper. These
results were announced in [PY3].

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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th