On the asymptotics of the scenery flow
Magnus Aspenberg Fredrik Ekström Tomas Persson Jörg Schmeling
Discrete & Continuous Dynamical Systems - A 2015, 35(7): 2797-2815 doi: 10.3934/dcds.2015.35.2797
We study the asymptotics of the scenery flow. We give corrected versions with proofs of a certain lemma by Hochman, and study some related phenomena.
keywords: interval map invariant measure fractal geometry Hausdorff dimension. Scenery flow
A notion of independence via moving targets
Jörg Schmeling
Discrete & Continuous Dynamical Systems - A 2006, 15(1): 269-280 doi: 10.3934/dcds.2006.15.269
We introduce a new notion of independence based on the Borel--Cantelli lemma. We study this characteristic in the context of i.i.d. stochastic processes and processes driven by equilibrium dynamics.
keywords: Thermodynamical formalism. Borel- Cantelli lemma non-i.i.d dynamical processes
Pointwise hyperbolicity implies uniform hyperbolicity
Boris Hasselblatt Yakov Pesin Jörg Schmeling
Discrete & Continuous Dynamical Systems - A 2014, 34(7): 2819-2827 doi: 10.3934/dcds.2014.34.2819
We provide a general mechanism for obtaining uniform information from pointwise data. For instance, a diffeomorphism of a compact Riemannian manifold with pointwise expanding and contracting continuous invariant cone families is an Anosov diffeomorphism, i.e., the entire manifold is uniformly hyperbolic.
keywords: nonuniform hyperbolicity Uniform hyperbolicity pointwise hyperbolicity.

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