Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unfolding a Bykov attractor: from an attracting torus to strange
  attractors   In this paper we present a comprehensive mechanism for the emergence of
strange attractors in a two-parametric family of differential equations acting
on a three-dimensional sphere. When both parameters are zero, its flow exhibits
an attracting heteroclinic network (Bykov network) made by two 1-dimensional
connections and one 2-dimensional separatrix between two hyperbolic
saddles-foci with different Morse indices. After slightly increasing both
parameters, while keeping the one-dimensional connections unaltered, we focus
our attention in the case where the two-dimensional invariant manifolds of the
equilibria do not intersect. Under some conditions on the parameters and on the
eigenvalues of the linearisation of the vector field at the saddle-foci, we
prove the existence of many complicated dynamical objects, ranging from an
attracting quasi-periodic torus to H\'enon-like strange attractors, as a
consequence of the Torus-Breakdown Theory. The mechanism for the creation of
horseshoes and strange attractors is also discussed. Theoretical results are
applied to show the occurrence of strange attractors in some analytic
unfoldings of a Hopf-zero singularity.

23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas