Displaying similar documents to “Characterization of ω -limit sets of continuous maps of the circle”

On the transitive and ω -limit points of the continuous mappings of the circle

David Pokluda (2002)

Archivum Mathematicum

Similarity:

We extend the recent results from the class 𝒞 ( I , I ) of continuous maps of the interval to the class 𝒞 ( 𝕊 , 𝕊 ) of continuous maps of the circle. Among others, we give a characterization of ω -limit sets and give a characterization of sets of transitive points for these maps.

Dense chaos

Ľubomír Snoha (1992)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

According to A. Lasota, a continuous function f from a real compact interval I into itself is called generically chaotic if the set of all points ( x , y ) , for which lim inf n → ∞ | f n ( x ) - f n ( y ) | = 0 and lim sup n → ∞ | f n ( x ) - f n ( y ) | > 0 , is residual in I × I . Being inspired by this definition we say that f is densely chaotic if this set is dense in I × I . A characterization of the generically chaotic functions is known. In the paper the densely chaotic functions are characterized and it is proved that in the class of piecewise monotone maps with finite number...

Sets of nondifferentiability for conjugacies between expanding interval maps

Thomas Jordan, Marc Kesseböhmer, Mark Pollicott, Bernd O. Stratmann (2009)

Fundamenta Mathematicae

Similarity:

We study differentiability of topological conjugacies between expanding piecewise C 1 + ϵ interval maps. If these conjugacies are not C¹, then their derivative vanishes Lebesgue almost everywhere. We show that in this case the Hausdorff dimension of the set of points for which the derivative of the conjugacy does not exist lies strictly between zero and one. Moreover, by employing the thermodynamic formalism, we show that this Hausdorff dimension can be determined explicitly in terms of the...

On Surjective Bing Maps

Hisao Kato, Eiichi Matsuhashi (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

In [7], M. Levin proved that the set of all Bing maps of a compact metric space to the unit interval is a dense G δ -subset of the space of all maps. In [6], J. Krasinkiewicz independently proved that the set of all Bing maps of a compact metric space to an n-dimensional manifold (n ≥ 1) is a dense G δ -subset of the space of maps. In [9], J. Song and E. D. Tymchatyn, solving some problems of J. Krasinkiewicz ([6]), proved that the set of all Bing maps of a compact metric space to a nondegenerate...

Kneading sequences for double standard maps

Michael Benedicks, Ana Rodrigues (2009)

Fundamenta Mathematicae

Similarity:

We investigate the symbolic dynamics for the double standard maps of the circle onto itself, given by f a , b ( x ) = 2 x + a + ( b / π ) s i n ( 2 π x ) ( m o d 1 ) , where b = 1 and a is a real parameter, 0 ≤ a < 1.

The converse problem for a generalized Dhombres functional equation

L. Reich, Jaroslav Smítal, M. Štefánková (2005)

Mathematica Bohemica

Similarity:

We consider the functional equation f ( x f ( x ) ) = ϕ ( f ( x ) ) where ϕ J → J is a given homeomorphism of an open interval J ⊂ ( 0 , ∞ ) and f ( 0 , ∞ ) → J is an unknown continuous function. A characterization of the class 𝒮 ( J , ϕ ) of continuous solutions f is given in a series of papers by Kahlig and Smítal 1998–2002, and in a recent paper by Reich et al. 2004, in the case when ϕ is increasing. In the present paper we solve the converse problem, for which continuous maps f ( 0 , ∞ ) → J , where J is an interval, there is an increasing homeomorphism ϕ of J such...

When ( E , σ ( E , E ' ) ) is a D F -space?

Dorota Krassowska, Wiesƚaw Śliwa (1992)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let ( E , t ) be a Hausdorff locally convex space. Either ( E , σ ( E , E ' ) ) or ( E ' , σ ( E ' , E ) ) is a D F -space iff E is of finite dimension (THEOREM). This is the most general solution of the problem studied by Iyahen [2] and Radenovič [3].