Some examples for the Poincaré and Painlevé problems
Some examples of cocycles with simple continuous singular spectrum
We study spectral properties of Anzai skew products defined by , where α is irrational and φ: → is a measurable cocycle. Precisely, we deal with the case where φ is piecewise absolutely continuous such that the sum of all jumps of φ equals zero. It is shown that the simple continuous singular spectrum of on the orthocomplement of the space of functions depending only on the first variable is a “typical” property in the above-mentioned class of cocycles, if α admits a sufficiently fast approximation....
Some examples of nonsingular Morse-Smale vector fields on
One wonders or not whether it is possible to determine the homotopy class of a vector field by examining some algebraic invariants associated with its qualitative behavior. In this paper, we investigate the algebraic invariants which are usually associated with the periodic solutions of non-singular Morse-Smale vector fields on the 3-sphere. We exhibit some examples for which there appears to be no correlation between the algebraic invariants of the periodic solutions and the homotopy classes of...
Some features of uncontinuable solutions of impulsive dynamical systems.
Some generic properties of concentration dimension of measure
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 .
Some lemmas about dynamical systems.
Some limit ratio theorem related to a real endomorphism in case of a neutral fixed point
Some model theory of SL(2,ℝ)
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.
Some models of Cahn-Hilliard equations in nonisotropic media
Some models of Cahn-Hilliard equations in nonisotropic media
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.
Some new cases of realization of spectral multiplicity function for ergodic transformations
Some new examples of recurrence and non-recurrence sets for products of rotations on the unit circle
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...
Some new results in state space decoupling of multivariable systems. I. A link between geometric approach and matrix methods
Some new results in state space decoupling of multivariable systems. II. Extensions to decoupling of systems with and output feedback decoupling
Some notes on topological recurrence.
Some novel ways of generating Cantor and Julia type sets
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.
Some numerical studies of dynamical systems
Some open problems in dynamical systems.
Some open problems in higher dimensional complex analysis and complex dynamics.
We present a collection of problems in complex analysis and complex dynamics in several variables.
Some orthogonal polynomials in four variables.