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.

scholarly journals Topological entropy and periodic points of a factor of a subshift of finite type

1986 ◽  
Vol 104 ◽  
pp. 117-127 ◽  
Author(s):  
Takashi Shimomura
Keyword(s):  
Finite Type ◽  
Topological Entropy ◽  
Compact Space ◽  
Metric Spaces ◽  
Periodic Points ◽  
Subshift Of Finite Type ◽  
Continuous Map ◽  
Continuous Maps ◽  
Definition Of ◽  
Uniformly Continuous

Let X be a compact space and f be a continuous map from X into itself. The topological entropy of f, h(f), was defined by Adler, Konheim and McAndrew [1]. After that Bowen [4] defined the topological entropy for uniformly continuous maps of metric spaces, and proved that the two entropies coincide when the spaces are compact. The definition of Bowen is useful in calculating entropy of continuous maps.

ON FINITE TYPE 3-MANIFOLD INVARIANTS I

1996 ◽  
Vol 05 (04) ◽  
pp. 441-461 ◽  
Author(s):  
STAVROS GAROUFALIDIS
Keyword(s):  
Vector Space ◽  
Finite Type ◽  
Commutative Algebra ◽  
Integral Homology ◽  
Knot Invariants ◽  
Finite Type Invariants ◽  
Definition Of ◽  
Type 3

Recently Ohtsuki [Oh2], motivated by the notion of finite type knot invariants, introduced the notion of finite type invariants for oriented, integral homology 3-spheres. In the present paper we propose another definition of finite type invariants of integral homology 3-spheres and give equivalent reformulations of our notion. We show that our invariants form a filtered commutative algebra. We compare the two induced filtrations on the vector space on the set of integral homology 3-spheres. As an observation, we discover a new set of restrictions that finite type invariants in the sense of Ohtsuki satisfy and give a set of axioms that characterize the Casson invariant. Finally, we pose a set of questions relating the finite type 3-manifold invariants with the (Vassiliev) knot invariants.

Recurrence in pairs

2008 ◽  
Vol 28 (4) ◽  
pp. 1135-1143 ◽  
Author(s):  
KAMEL HADDAD ◽  
WILLIAM OTT
Keyword(s):  
Finite Number ◽  
Finite Type ◽  
Sufficient Conditions ◽  
Dense Orbit ◽  
Subshift Of Finite Type

AbstractWe introduce and study the notion of weak product recurrence. Two sufficient conditions for this type of recurrence are established. We deduce that any point with a dense orbit in either the full one-sided shift on a finite number of symbols or a mixing subshift of finite type is weakly product recurrent. This observation implies that distality does not follow from weak product recurrence. We have therefore answered, in the negative, a question posed by Auslander and Furstenberg.

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