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Article Dans Une Revue Communications in Mathematical Physics Année : 2021

Regularity of Characteristic Exponents and Linear Response for Transfer Operator Cocycles

Résumé

We consider cocycles obtained by composing sequences of transfer operators with positive weights, associated with uniformly expanding maps (possibly having countably many branches) and depending upon parameters. Assuming $C^k$ regularity with respect to coordinates and parameters, we show that when the sequence is picked within a certain uniform family the top characteristic exponent and generator of top Oseledets space of the cocycle are $C^{k-1}$ in parameters. As applications, we obtain a linear response formula for the equivariant measure associated with random products of uniformly expanding maps, and we study the regularity of the Hausdorff dimension of a repeller associated with random compositions of one-dimensional cookie-cutters.

Dates et versions

hal-03191347 , version 1 (07-04-2021)

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Citer

Julien Sedro, Hans Henrik Rugh. Regularity of Characteristic Exponents and Linear Response for Transfer Operator Cocycles. Communications in Mathematical Physics, 2021, 383 (2), pp.1243-1289. ⟨10.1007/s00220-021-04019-9⟩. ⟨hal-03191347⟩
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