Convergence speed of a Ruelle operator associated with a non-uniformly expanding conformal dynamical system and a Dini potential

Yunping Jiang; Yuan-Ling Ye

doi:10.3934/dcds.2018206

Article Contents

2018, Volume 38, Issue 9: 4693-4713. Doi: 10.3934/dcds.2018206

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Convergence speed of a Ruelle operator associated with a non-uniformly expanding conformal dynamical system and a Dini potential

Yunping Jiang^1,2, and
Yuan-Ling Ye^3, ,

1.
Department of Mathematics, Queens College of the City University of New York (CUNY), Flushing, NY 11367-1597, USA
2.
Department of Mathematics, CUNY Graduate Center, 365 Fifth Avenue, New York, NY 10016, USA
3.
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China

* Corresponding author
* Corresponding author

Received: December 1, 2017

Published online: September 1, 2018

This material is based upon work supported by the National Science Foundation. Yunping Jiang is partially supported by a collaboration grant from the Simons Foundation (grant number 523341) and PSC-CUNY awards. Both the two authors are partially supported by a grant from NSFC (grant number 11571122).

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Abstract

We study the convergence speed of a Ruelle operator associated with a non-uniformly expanding conformal dynamical system and a Dini potential. Even without uniformly bounded distortion in this case, which makes the study much harder, we are still able to obtain a very nice estimation of the convergence speed under a certain quasi-gap condition.

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Mathematics Subject Classification: Primary: 37C30; Secondary: 37C40.

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References

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