Related papers: Ergodic properties of linked-twist maps
We investigate homeomorphisms of a compact interval, applied randomly. We consider this system as a skew product with the two-sided Bernoulli shift in the base. If on the open interval there is a metric in which almost all maps are…
We introduce characteristic functions for certain contractive liftings of row contractions. These are multi-analytic operators which classify the liftings up to unitary equivalence and provide a kind of functional model. The most important…
In this article we characterize monotone extensions of cw-expansive homeomorphisms of compact metric spaces. We study the topology of its quotient space in the case of a compact surface. These results are applied to prove that there are…
Topological invariants such as winding numbers and linking numbers appear as charges of topological solitons in diverse nonlinear physical systems described by a unit vector field defined on two and three dimensional manifolds. While the…
A gap in the proof of the main result in reference [1] in our original submission propagated into the constructions presented in the first version of our manuscript. In this version we give an alternative proof for the existence of…
We study transitive step skew-product maps modeled over a complete shift of $k$, $k\ge2$, symbols whose fiber maps are defined on the circle and have intermingled contracting and expanding regions. These dynamics are genuinely nonhyperbolic…
We derive gauge-invariant expressions for the twist $Tw$ and the linking number $Lk$ of a closed space curve, that are independent of the frame used to describe the curve, and hence characterize the intrinsic geometry of the curve. We are…
For a non-elementary subgroup of the mapping class group of a surface, we study its invariant Radon measures on the space of measured laminations, by classifying them on the recurrent measured laminations. In particular, given a…
Typical properties of measure space automorphisms with respect to the Halmos and Alpern-Tikhonov metrics are discussed.
If a map has k transitivity classes of vertices that are subject to the action of the automorphism group, it is said to be k-uniform. The classification of 1-uniform maps on the torus is known. In this article, we classify 2-uniform maps on…
We study measure-theoretical aspects of torus piecewise isometries. Not much is known about this type of dynamical systems, except for the special case of one-dimensional interval exchange mappings. The last case is fundamentally different…
For the generic continuous map and for the generic homeomorphism of the Cantor space, we study the dynamics of the induced map on the space of probability measures, with emphasis on the notions of Li-Yorke chaos, topological entropy,…
We analyze a class of piecewise linear parabolic maps on the torus, namely those obtained by considering a linear map with double eigenvalue one and taking modulo one in each component. We show that within this two parameter family of maps,…
We study genericity of dynamical properties in the space of homeomorphisms of the Cantor set and in the space of subshifts of a suitably large shift space. These rather different settings are related by a Glasner-King type correspondence:…
This paper is partly an exposition, and partly an extension of our work [1] to the multiparameter case. We consider certain classes of parametrized dynamically defined measures. These are push-forwards, under the natural projection, of…
We reduce the earlier known optimal shear parameter for which ergodicity is established in the linked twist map with two linear shears in opposite sense, in the most general setting. Further, here we obtain ergodicity with possibly only…
We show that the ergodicity of an aperiodic automorphism of a Lebesgue space is equivalent to the continuity of a certain map on a metric Boolean algebra. A related characterization is also presented for periodic and totally ergodic…
We provide conditions which guarantee that ergodic measures are dense in the simplex of invariant probability measures of a dynamical system given by a continuous map acting on a Polish space. Using them we study generic properties of…
In this paper, following J.Nielsen, we introduce a complete characteristic of orientation preserving periodic maps on the two-dimensional torus. All admissible complete characteristics were found and realized. In particular, each of classes…
After the surface theory of M\"obius geometry, this study concerns a pair of conformally immersed surfaces in $n$-sphere. Two new invariants $\theta$ and $\rho$ associated with them are introduced as well as the notion of touch and…