A variational functional E on Riemannian metrics vanishes precisely when geodesics realize prescribed unparametrised paths, and every conformal class on a surface admits a unique (up to homothety) conformally critical metric for E.
Ruelle, title title Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics
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A new linearized dynamics based on the anti-symmetric part of the stability matrix preserves phase space volume for non-Hamiltonian chaotic systems within a classical density matrix framework.
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Prescribing geodesics and a variational problem for Riemannian metrics
A variational functional E on Riemannian metrics vanishes precisely when geodesics realize prescribed unparametrised paths, and every conformal class on a surface admits a unique (up to homothety) conformally critical metric for E.
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Phase space volume preserving dynamics for non-Hamiltonian systems
A new linearized dynamics based on the anti-symmetric part of the stability matrix preserves phase space volume for non-Hamiltonian chaotic systems within a classical density matrix framework.