Positive transfer operators and decay of correlations

By Viviane Baladi. 2000

794 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ac9ee03516a48431f45a8cef9f55f0cd406117fa

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In Computational Theory and Mathematics

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In Statistical and Nonlinear Physics

Citations in the corpus

Smooth Anosov flows: Correlation spectra and stability (2007, background): “In more recent years, several authors have attempted to put forward a different approach to the study of hyperbolic dynamical systems based on the direct study of the transfer operator (see [1] for an introduction to the theory of transfer operators in dynamical systems).”
Bifurcations of stationary measures of random diffeomorphisms (2005, background): “The reader can consult [6, 45] for background on decay of correlations.”
RECURRENCE RATE IN RAPIDLY MIXING DYNAMICAL SYSTEMS (2004, methodology): “tems with a Young tower [16, 17], expanding maps with singularities such as in [13], some non-uniformly expanding maps [1], etc. The main reference for these questions is certainly the book by Baladi [2]. The reader will also ﬁnd in the review by Luzzatto [11] an exposition of the recent methods for”
THE DYNAMICAL BOREL-CANTELLI LEMMA FOR INTERVAL MAPS (2007, neutral): “See also [1] for a comprehensive reference.”
Frontiers of chaotic advection (2014, background): “Since A is a hyperbolic matrix, the exponential growth of |kAn| together with the exponential decay of Fourier coefficients yield superexponential decay of Cn (Baladi, 2000).”
A semi-invertible Oseledets Theorem with applications to transfer operator cocycles (2010, background): “The next lemma appears as an exercise in the deterministic case in Baladi’s book [3].”
Uniqueness of Invariant Measures for Place-Dependent Random Iterations of Functions (2002, background): “[13], [58], [55], [8], [26] and [3] for more on this and for an overview of further results in this field.”
A new look at the crossed-product of a C*-algebra by an endomorphism (2000, background): “Then the inverse image σ−1({y}) is finite and non-empty for each y ∈ X and the map L : C(X) → C(X) defined by L(f )|y = 1 #σ−1({y}) ∑ t∈X σ(t)=y f (t) for all f ∈ C(X), y ∈ X, is often called a transfer operator for the pair (X, σ) and has important uses in classical dynamics [20, 1].”
Expanding maps on Cantor sets and analytic continuation of zeta functions (2005, background): “See also [4] for a review of this type of results for more general expanding maps.”
On the spectrum of Farey and Gauss maps (2002, background): “Remark 6 The relevance of the above result issues from the following observation: the spectral radius of P in any reasonable Banach space of functions is equal to one (see [Ba1], [C]) so that according to Proposition 3.”