A dynamical version of the Bourgain-Fremlin-Talagrand dichotomy shows that the enveloping semigroup of a dynamical system is either very large and contains a topological copy of βN, or it is a “tame” topological space whose topology is determined by the convergence of sequences. In the latter case we say that the dynamical system is tame. We show that (i) a metric distal minimal system is tame ...

A dynamical version of the Bourgain-Fremlin-Talagrand dichotomy shows that the enveloping semigroup of a dynamical system is either very large and contains a topological copy of βN, or it is a “tame” topological space whose topology is determined by the convergence of sequences. In the latter case we say that the dynamical system is tame. We show that (i) a metric distal minimal system is tame ...

We consider the derivative nonlinear Schrodinger equation in one space dimension, posed both on line and circle. This model is known to be completely integrable $L^2$-critical with respect scaling. The first question we discuss whether ensembles of orbits $L^2$-equicontinuous initial data remain equicontinuous under evolution. prove that this true restriction $M(q)=\int |q|^2 < 4\pi$. conject...

We define a partition $\mathcal{P}_0$ and $\mathbb{Z}^2$-rotation ($\mathbb{Z}^2$-action defined by rotations) on 2-dimensional torus whose associated symbolic dynamical system is minimal proper subshift of the Jeandel-Rao aperiodic Wang shift 11 tiles. another $\mathcal{P}_\mathcal{U}$ $\mathbb{T}^2$ equal to 19 This proves that Markov for $\mathbb{T}^2$. prove in both cases toral maximal equi...

We prove a Desch-Schappacher type perturbation theorem for strongly continuous and locally equicontinuous one-parameter semigroups which are defined on a sequentially complete locally convex space.

We obtain sufficient conditions for commutative non-autonomous systems on certain metric spaces (not necessarily compact) to be topologically stable. In particular, we prove that: (i) Every mean equicontinuous, expansive system with strong average shadowing property is (ii) recurrently eventual (iii)

Motivated by Wooders, Cartwright, and Selten (2006), we consider games with a continuum of players and intermediate preferences. We show that any such game has a Nash equilibrium that induces a partition of the set of attributes into a bounded number of convex sets with the following property: all players with an attribute in the interior of the same element of the partition play the same actio...

This result suggests that every uniformity on X can be defined by means of a family of sets of real bounded continuous functions, and that important uniformities on X (such as precompact [l ] ones) are definable by means of "nice" sets of such functions. These and related problems are investigated here. A family J of sets of real functions will be said to separate a topological space X if for e...

In this article we study the arcwise connected component in the Pontryagin dual of an abelian topological group. It is clear that the set of continuous characters that can be lifted over the reals is contained in the arcwise connected component of the dual group. We show that the converse is true if all arcs in the character group are equicontinuous sets. This property is present in Pontryagin ...