DCDS
On the asymptotics of the scenery flow
Magnus Aspenberg Fredrik Ekström Tomas Persson Jörg Schmeling
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
DCDS
A notion of independence via moving targets
Jörg Schmeling
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
DCDS
Pointwise hyperbolicity implies uniform hyperbolicity
Boris Hasselblatt Yakov Pesin Jörg Schmeling
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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