A note on strange nonchaotic attractors

Keller G (1996)

Publication Type: Journal article, Original article

Publication year: 1996

Journal

Fundamenta Mathematicae Polskiej Akademii Nauk, Instytut Matematyczny (Polish Academy of Sciences, Institute of Mathematics)

Publisher: Polskiej Akademii Nauk, Instytut Matematyczny (Polish Academy of Sciences, Institute of Mathematics)

Book Volume: 151

Pages Range: 139-148

Journal Issue: Issue 2

Abstract

For a class of quasiperiodically forced time-discrete dynamical systems of two variables (θ, x) ∈ duoble-struct T sign¹ × ℝ+ with nonpositive Lyapunov exponents we prove the existence of an attractor Γ̄ with the following properties: 1. Γ̄ is the closure of the graph of a function x = φ(θ). It attracts Lebesgue-a.e. starting point in duoble-struct T sign¹ × 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 duoble-struct Tsign¹ × ℝ+ is Γ̄, but for a residual set of points in duoble-struct Tsign¹ × ℝ+ the omega limit is the circle {(θ, x) = 0} contained in Γ̄. 3. Γ̄ is the topological support of a BRS measure. The corresponding measure theoretical dynamical system is isomorphic to the forcing rotation.

Authors with CRIS profile

Gerhard Keller Professur für Angewandte Mathematik (Angewandte Analysis)

How to cite

APA:

Keller, G. (1996). A note on strange nonchaotic attractors. Fundamenta Mathematicae, 151(Issue 2), 139-148.

MLA:

Keller, Gerhard. "A note on strange nonchaotic attractors." Fundamenta Mathematicae 151.Issue 2 (1996): 139-148.

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