A Generic Property of Exact Magnetic Lagrangians
M\'ario Jorge Dias Carneiro, Alexandre Rocha
TL;DR
This paper demonstrates that for a broad class of Exact Magnetic Lagrangians, having finitely many static classes per cohomology class is a typical property, with implications for their dynamical behavior.
Contribution
It establishes the genericity of the finiteness of static classes in the set of Exact Magnetic Lagrangians and explores related dynamical consequences.
Findings
Finiteness of static classes is a generic property.
Dynamical consequences follow from this property.
Applicable to the set of Exact Magnetic Lagrangians.
Abstract
We prove that for the set of Exact Magnetic Lagrangians the property "There exist finitely many static classes for every cohomology class" is generic. We also prove some dynamical consequences of this property.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Mathematical Dynamics and Fractals · Geometry and complex manifolds