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Construction and applications of proximal maps for typical cocycles

Part of: Dynamical systems with hyperbolic behavior

Published online by Cambridge University Press:  10 February 2023

KIHO PARK Open the ORCID record for KIHO PARK [Opens in a new window]
KIHO PARK*
Affiliation:
KIAS, 85 Hoegiro, Dongdaemun-gu, Seoul 02455, Republic of Korea
*
e-mail: [email protected]
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Abstract

For typical cocycles over subshifts of finite type, we show that for any given orbit segment, we can construct a periodic orbit such that it shadows the given orbit segment and that the product of the cocycle along its orbit is a proximal linear map. Using this result, we show that suitable assumptions on the periodic orbits have consequences over the entire subshift.

Keywords

typical cocyclesdominated splittingsubadditive thermodynamic formalismLyapunov exponents

MSC classification

Primary: 37D25: Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) 37D30: Partially hyperbolic systems and dominated splittings 37D35: Thermodynamic formalism, variational principles, equilibrium states
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 44 , Issue 1 , January 2024 , pp. 204 - 235
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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