Melbourne, Ian and Gottwald, Georg A (2008) Power spectra for deterministic chaotic dynamical systems. Nonlinearity, vol.21 (No.1). pp. 179-189. doi:10.1088/0951-7715/21/1/010 ISSN 0951-7715.

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Abstract

We present results on the broadband nature of power spectra for large classes of discrete chaotic dynamical systems, including uniformly hyperbolic (Axiom A) diffeomorphisms and certain nonuniformly hyperbolic diffeomorphisms (such as the Henon map). Our results also apply to noninvertible maps, including Collet-Eckmann maps. For such maps (even the nonmixing ones) and Holder continuous observables, we prove that the power spectrum is analytic except for finitely many removable singularities, and that for typical observables the spectrum is nowhere zero. Indeed, we show that the power spectrum is bounded away from zero except for infinitely degenerate observables. For slowly mixing systems such as Pomeau-Manneville intermittency maps, where the power spectrum is at most finitely differentiable, nonvanishing of the spectrum remains valid provided the decay of correlations is summable.

Item Type:	Journal Article
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title:	Nonlinearity
Publisher:	Institute of Physics Publishing Ltd.
ISSN:	0951-7715
Official Date:	2008
Dates:	Date Event 2008 Published
Volume:	vol.21
Number:	No.1
Page Range:	pp. 179-189
DOI:	10.1088/0951-7715/21/1/010
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

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