Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dimension Reduction Near Periodic Orbits of Hybrid Systems   When the Poincar\'{e} map associated with a periodic orbit of a hybrid
dynamical system has constant-rank iterates, we demonstrate the existence of a
constant-dimensional invariant subsystem near the orbit which attracts all
nearby trajectories in finite time. This result shows that the long-term
behavior of a hybrid model with a large number of degrees-of-freedom may be
governed by a low-dimensional smooth dynamical system. The appearance of such
simplified models enables the translation of analytical tools from smooth
systems-such as Floquet theory-to the hybrid setting and provides a bridge
between the efforts of biologists and engineers studying legged locomotion.

21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex