ar X iv : m at h / 94 03 22 1 v 1 [ m at h . D S ] 5 M ar 1 99 4 INDUCING , SLOPES , AND CONJUGACY CLASSES
نویسندگان
چکیده
We show that the conjugacy class of an eventually expanding continuous piecewise affine interval map is contained in a smooth codimension 1 submanifold of parameter space. In particular conjugacy classes have empty interior. This is based on a study of the relation between induced Markov maps and ergodic theoretical behavior. Dept. of Mathematics, Northwestern University, Evanston, IL 60208-2730. Institute of Mathematical Sciences, SUNY at Stony Brook, Stony Brook, NY 11794-3651. I.B.M., Po Box 218, Yorktown Heights, NY 10598. 1 2 ROZA GALEEVA, MARCO MARTENS, AND CHARLES TRESSER
منابع مشابه
Cyclic Complexity of Words
We introduce and study a new complexity function on words, that we call cyclic complexity, which counts the number of conjugacy classes of factors of each given length. We extend the famous MorseHedlund theorem to the setting of cyclic complexity by showing that a word is ultimately periodic if and only if it has bounded cyclic complexity. Unlike most complexity functions, cyclic complexity dis...
متن کاملChaotic Unimodal and Bimodal Maps
We describe up to conjugacy all unimodal and bimodal maps that are chaotic, by giving necessary and sufficient conditions for unimodal and bimodal maps of slopes ±s to be transitive.
متن کاملThe Simultaneous Conjugacy Problem in Thompson’s Group F
Guba and Sapir asked, in their joint paper [3], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson’s group F . We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientationpreserving homeomorphisms of the unit interval with dyadic breakpoints and slopes tha...
متن کاملUniqueness of Parry Maps, and Invariants for Transitive Piecewise Monotonic Maps
Parry showed that every continuous transitive piecewise monotonic map τ of the interval is conjugate (by an order preserving homeomorphism) to a uniformly piecewise linear map T (i.e., one with slopes ±s). In the current article, it is shown that the map T is unique. This is proven by showing that any order-preserving conjugacy between two continuous transitive uniformly piecewise linear maps i...
متن کاملGains from diversification on convex combinations: A majorization and stochastic dominance approach
By incorporating both majorization theory and stochastic dominance theory, this paper presents a general theory and a unifying framework for determining the diversification preferences of risk-averse investors and conditions under which they would unanimously judge a particular asset to be superior. In particular, we develop a theory for comparing the preferences of different convex combination...
متن کامل