Non-transitive points and porosity

• Autorzy: T. K. Subrahmonian Moothathu
• Języki publikacji: EN

Abstrakty

EN

We establish that for a fairly general class of topologically transitive dynamical systems, the set of non-transitive points is very small when the rate of transitivity is very high. The notion of smallness that we consider here is that of σ-porosity, and in particular we show that the set of non-transitive points is σ-porous for any subshift that is a factor of a transitive subshift of finite type, and for the tent map of [0,1]. The result extends to some finite-to-one factor systems. We also show that for a family of piecewise monotonic transitive interval maps, the set of non-transitive points is σ-polynomially porous. We indicate how similar methods can be used to give sufficient conditions for the set of non-recurrent points and the set of distal pairs of a dynamical system to be very small.

Kategorie tematyczne

• 54H20: Topological dynamics
• 26A16: Lipschitz (H\"older) classes
• 37B10: Symbolic dynamics
• 37E05: Maps of the interval (piecewise continuous, continuous, smooth)
• 28A05: Classes of sets (Borel fields, σ -rings, etc.), measurable sets, Suslin sets, analytic sets

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2013
• Tom: 133
• Numer: 1
• Strony: 99-114

Daty

wydano

2013

Twórcy

autor

T. K. Subrahmonian Moothathu

• School of Mathematics and Statistics, University of Hyderabad, Hyderabad 500046, India

Identyfikatory

DOI

10.4064/cm133-1-7