We build an example of a non-transitive, dynamically coherent partially hyperbolic diffeomorphism f on a closed 3-manifold with exponential growth in its fundamental group such that f is not isotopic to the identity for all n ̸= 0. This example contradicts a conjecture in [HHU1]. The main idea is to consider a well-understood time-t map of a non-transitive Anosov flow and then carefully compose ...

If $X$ is an almost transitive Banach space with amenable isometry group (for example, if $X=L^p([0,1])$ $1\leq p \lt \infty $) and admits a uniformly continuous map $X\overset \phi \longrightarrow E$ into $E$ satisfying $$ \inf _{

A covalence sequence of a vertex-transitive map is a cyclic sequence of covalences around a vertex of the map. We explain the algebraic background for a study of the relationship between covalence sequences of maps on compact orientable surfaces and covalence sequences of (infinite) plane tessellations that both exhibit the same ‘level of transitivity’ of automorphism groups on vertices or edges.

A homeomorphism f of a manifold M is called H1-transitive if there is a transitive lift of an iterate of f to the universal Abelian cover M̃ . Roughly speaking, this means that f has orbits which repeatedly and densely explore all elements of H1(M). For a rel pseudo-Anosov map φ of a compact surface M we show that the following are equivalent: (a) φ is H1-transitive, (b) the action of φ on H1(M)...

We study countably piecewise continuous, piecewise monotone interval maps. We establish a necessary and sufficient criterion for the existence of a nondecreasing semiconjugacy to a map of constant slope in terms of the existence of an eigenvector of an operator acting on a space of measures. Then we give sufficient conditions under which this criterion is not satisfied. Finally, we give example...

‎darafsheh and assari in [normal edge-transitive cayley graphs on non-abelian groups of order 4p‎, ‎where $p$ is a prime number‎, ‎sci‎. ‎china math‎., ‎56 (1) (2013) 213-219.] classified the connected normal edge transitive and‎ ‎$frac{1}{2}-$arc-transitive cayley graph of groups of order $4p$‎. ‎in this paper we continue this work by classifying the‎ ‎connected cayley graph of groups of order...

Let R be a local Noetherian domain of positive characteristic. A theorem of Hochster and Huneke (1992) states that if R is excellent, then the absolute integral closure of R is a big Cohen-Macaulay algebra. We prove that if R is the homomorphic image of a Gorenstein local ring, then all the local cohomology (below the dimension) of such a ring maps to zero in a finite extension of the ring. The...

We investigate the interrelationships between the dynamical properties of commuting continuous maps of a compact metric space. Let X be a compact metric space. First we show the following. If τ : X → X is an expansive onto continuous map with the pseudo-orbit tracing property (POTP) and if there is a topologically mixing continuous map φ : X → X with τφ = φτ , then τ is topologically mixing. If...