Horseshoes for singly thermostated hamiltonians
Leo T. Butler
TL;DR
This paper proves the existence of horseshoe dynamics in certain thermostated Hamiltonian systems with one degree of freedom, under specific conditions on the system and thermostat.
Contribution
It establishes the presence of horseshoe structures in the flow of singly thermostated Hamiltonian systems, advancing understanding of their chaotic behavior.
Findings
Horseshoe dynamics exist under certain conditions
Conditions relate to the Hamiltonian and thermostat properties
Chaotic behavior can be rigorously demonstrated
Abstract
This note studies 1 and 2 degree of freedom hamiltonian systems that are thermostated by a single-variable thermostat. Under certain conditions on the hamiltonian and thermostat, the existence of a horseshoe in the flow of the thermostated system is proven.
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