Corridengum: Linear and fractional response for the SRB measure of smooth hyperbolic attractors and discontinuous observables (2017 Nonlinearity30 1204). (23rd June 2017)

• Record Type: Journal Article
• Authors: Baladi, Viviane; Kuna, Tobias; Lucarini, Valerio
• Is Part Of: Nonlinearity. Volume 30:Number 8(2017:Aug.)
• Page Start: C4
• Page End: C6
• Publication Date: 2017-06-23
• Subjects: linear response -- hyperbolic attractor -- transfer operator -- anisotropic space; 37C40 -- 37C30 -- 37D20; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aa7768
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: The first main result of Baladi et al (2017 Nonlinearity 30 1204–20) is modified as follows: For any θ in the Sobolev space H p r ( M ), with 1 < p < ∞ and 0 < r < 1 / p, the map t ↦ ∫ θ d ρ t is α -Hölder continuous for all α < r − | log J | / ( p | log ⁡ ν s | ) where J ⩽ 1 is the strongest volume contraction and ν s < 1 is the weakest contraction. This applies to θ ( x ) = h ( x ) Θ ( g ( x ) − a ) (for all α < 1 − | log J | / | log ⁡ ν s | ) for h and g smooth and Θ the Heaviside function, if a is not a critical value of g '.