Contact geometry in infinite dimensions
Fraser Aidan Kelvin Sanders
TL;DR
This paper extends contact geometry concepts to infinite-dimensional spaces, providing models for time-dependent and dissipative Hamiltonian systems, thus broadening the mathematical framework for such systems.
Contribution
It introduces the generalization of cosymplectic, contact, and cocontact manifolds to infinite dimensions and offers concrete examples of relevant Hamiltonian systems.
Findings
Successful generalization of contact geometry to infinite dimensions
Explicit models of time-dependent Hamiltonian systems
Application to dissipative systems
Abstract
We generalise the theories of cosymplectic, contact, and cocontact manifolds to the infinite-dimensional setting and calculate model examples of time-dependent and dissipative Hamiltonian systems.
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Taxonomy
TopicsControl and Stability of Dynamical Systems · Quantum chaos and dynamical systems · Geometric and Algebraic Topology