Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical Methods and Closed Orbits in the Kepler-Heisenberg Problem   The Kepler-Heisenberg problem is that of determining the motion of a planet
around a sun in the sub-Riemannian Heisenberg group. The sub-Riemannian
Hamiltonian provides the kinetic energy, and the gravitational potential is
given by the fundamental solution to the sub-Laplacian. This system is known to
admit closed orbits, which all lie within a fundamental integrable subsystem.
Here, we develop a computer program which finds these closed orbits using Monte
Carlo optimization with a shooting method, and applying a recently developed
symplectic integrator for nonseparable Hamiltonians. Our main result is the
discovery of a family of flower-like periodic orbits with previously unknown
symmetry types. We encode these symmetry types as rational numbers and provide
evidence that these periodic orbits densely populate a one-dimensional set of
initial conditions parametrized by the orbit's angular momentum. We provide
links to all code developed.

33
The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int