Rates of Recurrence for Z  q   and R  q   Extensions of Subshifts of Finite Type | Zendy

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Rates of Recurrence for Z q and R q Extensions of Subshifts of Finite Type

Author(s) -

Pollicott Mark,

Sharp Richard

Publication year - 1994

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/jlms/49.2.401

Subject(s) - conjecture , formalism (music) , complement (music) , type (biology) , mathematics , extension (predicate logic) , subshift of finite type , pure mathematics , computer science , programming language , chemistry , ecology , biology , art , musical , biochemistry , complementation , visual arts , gene , phenotype

In this note we give new asymptotic formulae for certain counting functions associated to the periodic behaviour of Z q and R q extensions of subshifts of finite type. In the case of the Z q extensions, these strengthen previous estimates of Marcus and Tuncel [ 9 ]. For both types of extension, our results complement the central limit type results of Lalley [ 6 ]. Our proof requires the application of ideas from thermodynamic formalism. Whilst developing this approach, in Section 2, we take the opportunity to present a counter‐example to a related conjecture of Coelho‐Filho [ 2 ].

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