Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Using invariant manifolds to construct symbolic dynamics for
  three-dimensional volume-preserving maps   Topological techniques are powerful tools for characterizing the complexity
of many dynamical systems, including the commonly studied area-preserving maps
of the plane. However, the extension of many topological techniques to higher
dimensions is filled with roadblocks preventing their application. This article
shows how to extend the homotopic lobe dynamics (HLD) technique, previously
developed for 2D maps, to volume-preserving maps of a three-dimensional phase
space. Such maps are physically relevant to particle transport by
incompressible fluid flows or by magnetic field lines. Specifically, this
manuscript shows how to utilize two-dimensional stable and unstable invariant
manifolds, intersecting in a heteroclinic tangle, to construct a symbolic
representation of the topological dynamics of the map. This symbolic
representation can be used to classify system trajectories and to compute
topological entropy. We illustrate the salient ideas through a series of
examples with increasing complexity. These examples highlight new features of
the HLD technique in 3D. Ultimately, in the final example, our technique
detects a difference between the 2D stretching rate of surfaces and the 1D
stretching rate of curves, illustrating the truly 3D nature of our approach.

34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
3
The categories of this paper are: physics
2
The categories of this paper are: math
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph