Quantitative Quasiperiodicity

  title={Quantitative Quasiperiodicity},
  author={Suddhasattwa Das and Yoshitaka Saiki and Evelyn Sander and James A. Yorke},
The Birkhoff Ergodic Theorem concludes that time averages, i.e., Birkhoff averages, BN(f) ∶= Σ n=0 f(xn)/N of a function f along a length N ergodic trajectory (xn) of a function T converge to the space average ∫ fdμ, where μ is the unique invariant probability measure. Convergence of the time average to the space average is slow. We use a modified average of f(xn) by giving very small weights to the “end” terms when n is near 0 or N − 1. When (xn) is a trajectory on a quasiperiodic torus and f… Expand
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