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2006, Volume 14, Issue 3: 409-417. Doi: 10.3934/dcds.2006.14.409
This issue Previous Article Vertex maps for trees: Algebra and periods of periodic orbits Next Article Unstable manifolds and Hölder structures associated with noninvertible maps

Necessary and sufficient conditions for semi-uniform ergodic theorems and their applications

  • 1.

    Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080

  • 2.

    School of Mathematical Sciences, Peking University, Beijing, 100871

  • 3.

    School of Sciences, Beihang University, Beijing, 100083

Received:  July 2004
Revised:  September 2005
Published:  September 2006
Abstract Related Papers Cited by
    Abstract
  • It has been established one-side uniform convergence in both the Birkhoff and sub-additive ergodic theorems under conditions on growth rates with respect to all the invariant measures. In this paper we show these conditions are both necessary and sufficient. These results are applied to study quasiperiodically forced systems. Some meaningful geometric properties of invariant sets of such systems are presented. We also show that any strange compact invariant set of a $\mathcal{C}^1$ quasiperiodically forced system must support an invariant measure with a non-negative normal Lyapunov exponent.
    Mathematics Subject Classification: 28D05, 54H20, 58D05 (primary), 37D45, 37C70 (secondary).

    Citation:
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