Detecting topological transitivity of piecewise monotone interval maps☆☆Partially supported by FCT/POCTI/FEDER.
نویسندگان
چکیده
منابع مشابه
Topological Conjugacy and Transitivity for a Class of Piecewise Monotone Maps of the Interval
We say that a continuous map / of a compact interval to itself is linear Markov if it is piecewise linear, and the set of all fk(x), where k > 0 and x is an endpoint of a linear piece, is finite. We provide an effective classification, up to topological conjugacy, for linear Markov maps and an effective procedure for determining whether such a map is transitive. We also consider expanding Marko...
متن کاملRoots of Continuous Piecewise Monotone Maps of an Interval
We shall consider slightly more general problems. Namely, we shall investigate the existence of continuous: piecewise monotone, piecewise strictly monotone, and piecewise linear n-th roots of interval maps which have a continuous n-th root. Here by an n-th root of f we mean a map g such that f = g (g is the n-th iterate of g). A continuous map f : I → J , where I, J are closed intervals, is pie...
متن کاملConvergence of the natural approximations of piecewise monotone interval maps.
We consider piecewise monotone interval mappings which are topologically mixing and satisfy the Markov property. It has previously been shown that the invariant densities of the natural approximations converge exponentially fast in uniform pointwise topology to the invariant density of the given map provided its derivative is piecewise Lipshitz continuous. We provide an example of a map which i...
متن کاملTopological Transitivity and Strong Transitivity
We discuss the relation between (topological) transitivity and strong transitivity of dynamical systems. We show that a transitive and open self-map of a compact metric space satisfying a certain expanding condition is strongly transitive. We also prove a couple of results for interval maps; for example it is shown that a transitive piecewise monotone interval map is strongly transitive.
متن کاملTopological transitivity
The concept of topological transitivity goes back to G. D. Birkhoff [1]
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2005
ISSN: 0166-8641
DOI: 10.1016/j.topol.2005.01.002