Journal ArticleDOI
On the rate of convergence to equilibrium in one-dimensional systems
TLDR
In this paper, the spectral radius of the Perron-Frobenius operator for piecewise expanding transformations is derived and the speed of convergence to equilibrium in such one-dimensional systems is analyzed.Abstract:
We determine the essential spectral radius of the Perron-Frobenius-operator for piecewise expanding transformations considered as an operator on the space of functions of bounded variation and relate the speed of convergence to equilibrium in such one-dimensional systems to the greatest eigenvalues of generalized Perron-Frobenius-operators of the transformations (operators which yield singular invariant measures).read more
Citations
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Journal Article
Stability of the spectrum for transfer operators
TL;DR: In this article, the isolated eigenvalues of transfer operators satisfying the Lasota-Yorke type inequality under a broad class of random and nonrandom perturbations including Ulam-type discretizations are proved.
Journal ArticleDOI
Banach spaces adapted to Anosov systems
TL;DR: In this article, the spectral properties of the Ruelle-Perron-Frobenius operator associated to an Anosov map on classes of functions with high smoothness were studied.
Journal ArticleDOI
On the spectra of randomly perturbed expanding maps
Viviane Baladi,Lai Sang Young +1 more
TL;DR: In this article, the authors consider small random perturbations of expanding and piecewise expanding maps and prove the robustness of their invariant densities and rates of mixing by proving the spectra of their Perron-Frobenius operators.
Journal ArticleDOI
Chaotic complex spreading sequences for asynchronous DS-CDMA. Part II. Some theoretical performance bounds
TL;DR: Mazzini et al. as discussed by the authors evaluated the impact of chaotic spreading codes on communication systems with asynchronous Code Division Multiple Access (CDMA) and provided analytical bounds on the expected partial cross correlation between spreading sequences obtained by quantizing and repeating a chaotic time series.
Journal ArticleDOI
Statistical modeling of discrete-time chaotic processes-basic finite-dimensional tools and applications
TL;DR: Experimental evidence shows that the availability of statistical tools enables the design of chaos-based systems which favorably compare with analogous nonchaos-based counterparts.
References
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Journal ArticleDOI
Entropy of piecewise monotone mappings
Michał Misiurewicz,W. Szlenk +1 more
TL;DR: In this paper, the conditions générales d'utilisation (http://www.emath.numdam.org/conditions) of the Astérisque collection of the Société mathématique de France are described.
Book ChapterDOI
Ergodic Properties of Invariant Measures for Piecewise Monotonic Transformations
Franz Hofbauer,Gerhard Keller +1 more
TL;DR: In this article, different kinds of invariant measures for certain classes of piecewise monotonic transformations have been considered and the Perron-Frobenius-operator plays an important role.
Journal ArticleDOI
A variational principle for the pressure of continuous transformations.
TL;DR: In this paper, Dinaburg and Goodman proved the variational principle for a continuous Zn action on a compact metric space, without these assumptions (Theorem 4.1).