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Currently displaying 1 – 11 of 11

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Piecewise Monotonic Transformations and Exactness

Gerhard Keller — 1978

Publications mathématiques et informatique de Rennes

Stochastic Stability in Some Chaotic Dynamical Systems.

Gerhard Keller — 1982

Monatshefte für Mathematik

Lifting Measures to Markov Extensions.

Gerhard Keller — 1989

Monatshefte für Mathematik

A note on dynamical zeta functions for S-unimodal maps

Gerhard Keller — 2000

Colloquium Mathematicae

Let f be a nonrenormalizable S-unimodal map. We prove that f is a Collet-Eckmann map if its dynamical zeta function looks like that of a uniformly hyperbolic map.

A note on strange nonchaotic attractors

Gerhard Keller — 1996

Fundamenta Mathematicae

For a class of quasiperiodically forced time-discrete dynamical systems of two variables (θ,x) ∈ $T^{1} \times ℝ_{+}$ with nonpositive Lyapunov exponents we prove the existence of an attractor Γ̅ with the following properties: 1. Γ̅ is the closure of the graph of a function x = ϕ(θ). It attracts Lebesgue-a.e. starting point in $T^{1} \times ℝ_{+}$ . The set θ:ϕ(θ) ≠ 0 is meager but has full 1-dimensional Lebesgue measure. 2. The omega-limit of Lebesgue-a.e point in $T^{1} \times ℝ_{+}$ is $Γ ̅$ , but for a residual set of points in $T^{1} \times ℝ_{+}$ the omega limit is the...