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Concave Toric Domains in Stark-type Mechanical Systems

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arxiv 2311.08912 v1 pith:CPEK46KV submitted 2023-11-15 math.DS math-phmath.MP

Airi Takeuchi , Lei Zhao This is my paper · ORCID
classification math.DSmath-phmath.MP
keywords concavedomainstoricboundedcriteriaenergymechanicalproblem
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It has been shown in [Frauenfelder, 2023] that the bounded component of the energy surface of the planer Stark problem after the Levi-Civita transformation are concave toric domains. In this paper, we present a different approach on the problem of determining concave toric domains in a family of integrable natural mechanical problems in the plane based on the computation of action-variables. We give criteria on the potentials for the bounded components of the energy hypersurfaces to be concave toric domains and apply these criteria to a class of problems.

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