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Title: Computing Reeb dynamics on four-dimensional convex polytopes

We study the combinatorial Reeb flow on the boundary of a four-dimensional convex polytope. We establish a correspondence between "combinatorial Reeb orbits" for a polytope, and ordinary Reeb orbits for a smoothing of the polytope, respecting action and Conley-Zehnder index. One can then use a computer to find all combinatorial Reeb orbits up to a given action and Conley-Zehnder index. We present some results of experiments testing Viterbo's conjecture and related conjectures. In particular, we have found some new examples of polytopes with systolic ratio \begin{document}$ 1 $\end{document}.

 
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Award ID(s):
2005437
PAR ID:
10300468
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Journal of Computational Dynamics
Volume:
0
Issue:
0
ISSN:
2158-2505
Page Range / eLocation ID:
0
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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