Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discontinuity induced bifurcations of non-hyperbolic cycles in nonsmooth
  systems   We analyse three codimension-two bifurcations occurring in nonsmooth systems,
when a non-hyperbolic cycle (fold, flip, and Neimark-Sacker cases, both in
continuous- and discrete-time) interacts with one of the discontinuity
boundaries characterising the system's dynamics. Rather than aiming at a
complete unfolding of the three cases, which would require specific assumptions
on both the class of nonsmooth system and the geometry of the involved
boundary, we concentrate on the geometric features that are common to all
scenarios. We show that, at a generic intersection between the smooth and
discontinuity induced bifurcation curves, a third curve generically emanates
tangentially to the former. This is the discontinuity induced bifurcation curve
of the secondary invariant set (the other cycle, the double-period cycle, or
the torus, respectively) involved in the smooth bifurcation. The result can be
explained intuitively, but its validity is proven here rigorously under very
general conditions. Three examples from different fields of science and
engineering are also reported.

18
The categories of this paper are: econ
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph