Equilibrium states for piecewise monotonic transformations
1982 ◽
Vol 2
(1)
◽
pp. 23-43
◽
Keyword(s):
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.
2000 ◽
Vol 20
(5)
◽
pp. 1495-1518
◽
Keyword(s):
1997 ◽
Vol 17
(4)
◽
pp. 977-1000
◽
2000 ◽
Vol 130
(5)
◽
pp. 1045-1079
◽
2013 ◽
Vol 35
(3)
◽
pp. 835-853
◽
2007 ◽
Vol 54
(2)
◽
pp. 183-191
◽