Autonomous Hamiltonian flows, Hofer’s geometry and persistence modules

Leonid Polterovich; Egor Shelukhin

doi:10.1007/s00029-015-0201-2

Autonomous Hamiltonian flows, Hofer’s geometry and persistence modules

Selecta Mathematica ◽

10.1007/s00029-015-0201-2 ◽

2015 ◽

Vol 22 (1) ◽

pp. 227-296 ◽

Cited By ~ 12

Author(s):

Leonid Polterovich ◽

Egor Shelukhin

Keyword(s):

Hamiltonian Flows ◽

Persistence Modules

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Homological Algebra for Persistence Modules

Foundations of Computational Mathematics ◽

10.1007/s10208-020-09482-9 ◽

2021 ◽

Author(s):

Peter Bubenik ◽

Nikola Milićević

Keyword(s):

Homological Algebra ◽

Persistence Modules

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Gaussian Model for Chaotic Instability of Hamiltonian Flows

Physical Review Letters ◽

10.1103/physrevlett.74.375 ◽

1995 ◽

Vol 74 (3) ◽

pp. 375-378 ◽

Cited By ~ 88

Author(s):

Lapo Casetti ◽

Roberto Livi ◽

Marco Pettini

Keyword(s):

Gaussian Model ◽

Hamiltonian Flows

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Chain recurrence, growth rates and ergodic limits

Ergodic Theory and Dynamical Systems ◽

10.1017/s0143385707000363 ◽

2007 ◽

Vol 27 (5) ◽

pp. 1509-1524 ◽

Cited By ~ 5

Author(s):

FRITZ COLONIUS ◽

ROBERTA FABBRI ◽

RUSSELL JOHNSON

Keyword(s):

Lyapunov Exponents ◽

Growth Rates ◽

General Linear ◽

Chain Recurrence ◽

Hamiltonian Flows ◽

Rotation Numbers ◽

Linear Flows

AbstractAverages of functionals along trajectories are studied by evaluating the averages along chains. This yields results for the possible limits and, in particular, for ergodic limits. Applications to Lyapunov exponents and to concepts of rotation numbers of linear Hamiltonian flows and of general linear flows are given.

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