Let be a compact quasi self-similar set in a complete metric space and let denote the space of all probability measures on , endowed with the Fortet-Mourier metric. We will show that for a typical (in the sense of Baire category) measure in the lower concentration dimension is equal to , while the upper concentration dimension is equal to the Hausdorff dimension of .
We study the action of G = SL(2,ℝ), viewed as a group definable in the structure M = (ℝ,+,×), on its type space . We identify a minimal closed G-flow I and an idempotent r ∈ I (with respect to the Ellis semigroup structure * on ). We also show that the “Ellis group” (r*I,*) is nontrivial, in fact it is the group with two elements, yielding a negative answer to a question of Newelski.
We derive in this article some models of Cahn-Hilliard equations in nonisotropic media. These models, based on constitutive equations introduced by Gurtin in [19], take the work of internal microforces and also the deformations of the material into account. We then study the existence and uniqueness of solutions and obtain the existence of finite dimensional attractors.
We study recurrence and non-recurrence sets for dynamical systems on compact spaces, in particular for products of rotations on the unit circle . A set of integers is called -Bohr if it is recurrent for all products of rotations on , and Bohr if it is recurrent for all products of rotations on . It is a result due to Katznelson that for each there exist sets of integers which are -Bohr but not -Bohr. We present new examples of -Bohr sets which are not Bohr, thanks to a construction which...
It is a survey article showing how an enhanced version of the Banach contraction principle can lead to generalizations of attractors of iterated function systems and to Julia type sets.
We present a collection of problems in complex analysis and complex dynamics in several variables.
We discuss the existence of closed geodesic on a Riemannian manifold and the existence of periodic solution of second order Hamiltonian systems.
We are interested in deformations of Baker domains by a pinching process in curves. In this paper we deform the Fatou function , depending on the curves selected, to any map of the form , p/q a rational number. This process deforms a function with a doubly parabolic Baker domain into a function with an infinite number of doubly parabolic periodic Baker domains if p = 0, otherwise to a function with wandering domains. Finally, we show that certain attracting domains can be deformed by a pinching...
We present some regularity properties of periodic solutions to a class of singular potential problems and we discuss the existence of a regular solution.