Topological Pressure of Poincare Recurrence Set

Fractals ◽  
2021 ◽  
Author(s):  
Yu Pei ◽  
Ercai Chen ◽  
Kui Yao
Keyword(s):  
Topological Pressure ◽  
Poincare Recurrence ◽  
Poincaré Recurrence

SPECTRA OF RECURRENCE DIMENSION FOR ADIC SYSTEMS

2002 ◽  
Vol 02 (04) ◽  
pp. 599-607 ◽  
Author(s):  
VÍCTOR F. SIRVENT
Keyword(s):  
Finite Type ◽  
Subshift Of Finite Type ◽  
Poincare Recurrence ◽  
Definition Of ◽  
Poincaré Recurrence

We compute the spectra of the recurrence dimension for adic systems and sub-adic systems. This dimension is characterized by the Poincaré recurrence of the system, and known in the literature as Afraimovich–Pesin dimension. These spectra are invariant under bi-Lipschitz transformations. We show that there is a duality between the spectra of an adic system and the corresponding subshift of finite type. We also consider Billingsley-like definition of the spectra of the recurrence dimension.

Sign in / Sign up

Export Citation Format

Share Document