Anisotropic Sobolev spaces and dynamical transfer operators: C

By Viviane Baladi. 2004

60 citations recorded by the source corpus.

We consider a smooth Anosov diffeomorphism with a smooth dynamical foliation. We show upper bounds on the essential spectral radius of its transfer operator acting on anisotropic Sobolev spaces. (Such bounds are related to the essential decorrelation rate for the SRB measure.) We compare our results to the estimates of Kitaev on the domain of holomorphy of dynamical Fredholm determinants for differentiable dynamics.

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Citations in the corpus

Banach spaces adapted to Anosov systems (2004, background): “See [ 4 ] for a very recent attempt, based on Fourier analysis, in a very special case.”
Quenched CLT for random toral automorphism (2007, background): “Instead of appealing to the general theory developed in [6, 4 , 12, 5, 13] we will take advantage of the simplicity of the present setting and introduce explicitly a particularly simple version of such a theory.”
Ruelle zeta function at zero for surfaces (2016, methodology): “References [Ba] Viviane Baladi, Anisotropic Sobolev spaces and dynamical transfer operators: C∞ foliations, Algebraic and topological dynamics, 123–135, Contemp.”
Good Banach spaces for piecewise hyperbolic maps via interpolation (2007, methodology): “Our proof extends the results of [ 4 ] to C1+α Anosov diffeomorphisms with C1+α stable and/or unstable distributions, and general Cα weights (see Remark 27).”
Banach spaces for piecewise cone hyperbolic maps (2009, background): “Let us now describe briefly this space H, which generalizes the spaces of [1, 2].”
Smooth Anosov flows: Correlation spectra and stability (2007, background): “The recent papers [19, 18, 12, 2, 3, 20, 9, 7, 21, 4, 13], have shown that such an approach yields a simpler and far reaching alternative to the more traditional point of view based on Markov partitions.”
Fredholm determinants, Anosov maps and Ruelle resonances (2005, background): “Lemma 2.9 is proven in section 3 while Proposition 2.1, proven in section 4, states the existence of the adapted spaces.”
The semiclassical zeta function for geodesic flows on negatively curved manifolds (2013, background): “Viviane Baladi, Anisotropic Sobolev spaces and dynamical transfer operators: C8 foliations, Algebraic and topological dynamics, Contemp.”