# American Institute of Mathematical Sciences

August  2018, 38(8): 3977-3991. doi: 10.3934/dcds.2018173

## Continuity of spectral radius over hyperbolic systems

 1 School of Mathematical Sciences, Soochow University, Suzhou 215006, China 2 Department of Mathematics, East China Normal University, Shanghai 200062, China

** Corresponding author: Gang Liao was partially supported by NSFC (11701402, 11790274), BK 20170327 and Jiangsu province "Double Plan"

*Yongluo Cao was partially supported by NSFC (11771317, 11790274), Science and Technology Commission of Shanghai Municipality (18dz22710000)

Received  October 2017 Revised  February 2018 Published  May 2018

The continuity of joint and generalized spectral radius is proved for Hölder continuous cocycles over hyperbolic systems. We also prove the periodic approximation of Lyapunov exponents for non-invertible non-uniformly hyperbolic systems, and establish the Berger-Wang formula for general dynamical systems.

Citation: Rui Zou, Yongluo Cao, Gang Liao. Continuity of spectral radius over hyperbolic systems. Discrete & Continuous Dynamical Systems - A, 2018, 38 (8) : 3977-3991. doi: 10.3934/dcds.2018173
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