The specification property

1976 ◽  
pp. 193-209
Author(s):  
Manfred Denker ◽  
Christian Grillenberger ◽  
Karl Sigmund
Keyword(s):  
Specification Property

scholarly journals Equilibrium states for piecewise monotonic transformations

1982 ◽  
Vol 2 (1) ◽  
pp. 23-43 ◽  
Author(s):  
Franz Hofbauer ◽  
Gerhard Keller
Keyword(s):  
Periodic Orbits ◽  
Bounded Variation ◽  
Critical Points ◽  
Equilibrium States ◽  
Absolutely Continuous ◽  
Specification Property ◽  
Ergodic Properties ◽  
Piecewise Monotonic

AbstractWe show that equilibrium states μ of a function φ on ([0,1], T), where T is piecewise monotonic, have strong ergodic properties in the following three cases:(i) sup φ — inf φ <htop(T) and φ is of bounded variation.(ii) φ satisfies a variation condition and T has a local specification property.(iii) φ = —log |T′|, which gives an absolutely continuous μ, T is C2, the orbits of the critical points of T are finite, and all periodic orbits of T are uniformly repelling.

Generalized Specification Property and Distributional Chaos

2003 ◽  
Vol 13 (07) ◽  
pp. 1683-1694 ◽  
Author(s):  
F. Balibrea ◽  
B. Schweizer ◽  
A. Sklar ◽  
J. Smítal
Keyword(s):  
Compact Interval ◽  
Limit Set ◽  
Distributional Chaos ◽  
Specification Property ◽  
Continuous Map ◽  
Basic Set ◽  
Made In

Let f be a continuous map from a compact interval into itself. Continuing the work begun by Schweizer and Smítal [1994], we prove that the restriction of f to any basic set (i.e. any nonsolenoidal, infinite, maximal ω-limit set) satisfies a generalization of the specification property. We apply this generalization to establish several conjectures made in the abovementioned paper, e.g. the fact that distributional chaos is stable.

scholarly journals Shift spaces, ω-chaos and specification property

2009 ◽  
Vol 156 (18) ◽  
pp. 2979-2985 ◽  
Author(s):  
M. Lampart ◽  
P. Oprocha
Keyword(s):  
Shift Spaces ◽  
Specification Property
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