Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dissecting a resonance wedge on heteroclinic bifurcations   This article studies routes to chaos occurring within a resonance wedge for a
3-parametric family of differential equations acting on a 3-sphere. Our
starting point is an autonomous vector field whose flow exhibits a weakly
attracting heteroclinic network made by two 1-dimensional connections and a
2-dimensional separatrix between two equilibria with different Morse indices.
After changing the parameters, while keeping the 1-dimensional connections
unaltered, we concentrate our study in the case where the 2-dimensional
invariant manifolds of the equilibria do not intersect. We derive the first
return map near the ghost of the attractor and we reduce the analysis of the
system to a 2-dimensional map on the cylinder. Complex dynamical features arise
from a discrete-time Bogdanov-Takens singularity, which may be seen as the
organizing center by which one can obtain infinitely many attracting tori,
strange attractors, infinitely many sinks and non-trivial contracting wandering
domains. These dynamical phenomena occur within a structure that we call
resonance wedge. As an application, we may see the "classical" Arnold tongue as
a projection of a resonance wedge. The results are general, extend to other
contexts and lead to a fine-tuning of the theory.

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The categories of this paper are: atom-ph
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex