Abstract
We consider suspension (semi)flows over \({C}^{1+\alpha }\) full-branch Markov piecewise expanding interval maps and piecewise hyperbolic maps and prove exponential decay of correlations with respect to Gibbs measures associated with piecewise Hölder continuous potentials. As a consequence, typical codimension one attractors of \(C^{1+\alpha }\) Axiom A flows have exponential decay of correlations with respect to any equilibrium state associated to Hölder continuous potentials. In the case of suspension semiflows over piecewise expanding interval maps, the argument uses a construction of certain partitions which are adapted to Gibbs measures, even those for which the Federer property fails.
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Acknowledgements
This work is part of the first author PhD thesis carried out at Federal University of Bahia (Salvador—Bahia). DD was supported by CAPES-Brazil. PV was partially supported by CMUP (UID/MAT/00144/2019), which is funded by FCT with national (MCTES) and European structural funds through the programs FEDER, under the partnership agreement PT2020, and by Fundação para a Ciência e Tecnologia (FCT)—Portugal—through the Grant CEECIND/03721/2017 of the Stimulus of Scientific Employment, Individual Support 2017 Call. The authors are grateful to Ian Melbourne for useful comments.
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Communicated by Dmitry Dolgopyat.
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Daltro, D., Varandas, P. Exponential Decay of Correlations for Gibbs Measures and Semiflows over \(C^{1+\alpha }\) Piecewise Expanding Maps. Ann. Henri Poincaré 22, 2137–2159 (2021). https://doi.org/10.1007/s00023-020-00991-5
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DOI: https://doi.org/10.1007/s00023-020-00991-5