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Gasquet, Claude; Witomski, Patrick

doi:10.1007/978-1-4612-1598-1_37

Fourier Analysis and Applications 1999

DOI: 10.1007/978-1-4612-1598-1_37

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Claude Gasquet

Patrick Witomski²

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Super convergence of ergodic averages for quasiperiodic orbits

Das

Yorke

2018

Nonlinearity

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The Birkhoff Ergodic Theorem asserts that time averages of a function evaluated along a trajectory of length N converge to the space average, the integral of f , as N → ∞, for ergodic dynamical systems. But that convergence can be slow. Instead of uniform averages that assign equal weights to points along the trajectory, we use an average with a non-uniform distribution of weights, weighing the early and late points of the trajectory much less than those near the midpoint N 2. We show that in quasiperiodic dynamical systems, our weighted averages converge far faster provided f is sufficiently differentiable. This result can be applied to obtain efficient numerical computation of rotation numbers, invariant densities and conjugacies of quasiperiodic systems.

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Super convergence of ergodic averages for quasiperiodic orbits

Das

Yorke

2018

Nonlinearity

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show abstract

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Cited by 1 publication

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Super convergence of ergodic averages for quasiperiodic orbits

Super convergence of ergodic averages for quasiperiodic orbits

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