Smooth Anosov flows: Correlation spectra and stability

By Oliver Butterley, C. Liverani. 2007

202 citations recorded by the source corpus.

By introducing appropriate Banach spaces one can study the spectral properties of the generator of the semigroup defined by an Anosov flow. Consequently, it is possible to easily obtain sharp results on the Ruelle resonances and the differentiability of the SRB measure.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/878eb9e2fcc727fe1a00c3a6d08b9acfdd54d7d3

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Citations in the corpus

Differentiation of SRB states for hyperbolic flows (2004, background): “Since this paper was written in 2004, the relevant reference [34] has appeared.”
A review of linear response theory for general differentiable dynamical systems (2009, background): “A different proof has been given in [11] in the case of Anosov flows.”
Data-driven non-Markovian closure models (2014, background): “Such considerations require typically spaces that take into account the stable and unstable manifolds of the attractor, when the latter supports a Sinai-Bowen-Ruelle measure; see, for instance, [110] in the case of Anosov flows.”
Anosov flows and dynamical zeta functions (2012, methodology): “4 in [10] to decompose each v ∈ V℘+q(φt(Wβ,Gxk,Fk )) as v = v s + v + v where v is tangent to φt(Wβ,Gxk,Fk ), v u is “close” to the unstable direction and v is the component in the flow direction.”
Linear response, or else (2014, background): “In the present note, we do not discuss linear response for continuous time dynamics [17, 50], or for dynamical systems in infinite dimensions (such as coupled map lattices [27, 28]).”
Small eigenvalues of the Laplacian for algebraic measures in moduli space, and mixing properties of the Teichmüller flow (2010, background): “This kind of arguments has been developed in recent years for Anosov maps or ﬂows in compact manifolds and has proved very fruitful (see among others [Liv04, GL06, BT07, BL07]).”