Discrete dynamics of complex systems.
Discrete Euler-Poincaré and Euler Poincaré-Poisson equations for semidirect products and principal bundles.
Discrete geometry and numeration
Discrete isothermic surfaces.
Discrete Ljapunov functionals and -limit sets
Discretization and Morse-Smale dynamical systems on planar discs.
Disjointness of the convolutionsfor Chacon's automorphism
The purpose of this paper is to show that if σ is the maximal spectral type of Chacon’s transformation, then for any d ≠ d’ we have . First, we establish the disjointness of convolutions of the maximal spectral type for the class of dynamical systems that satisfy a certain algebraic condition. Then we show that Chacon’s automorphism belongs to this class.
Disjointness properties for Cartesian products of weakly mixing systems
For n ≥ 1 we consider the class JP(n) of dynamical systems each of whose ergodic joinings with a Cartesian product of k weakly mixing automorphisms (k ≥ n) can be represented as the independent extension of a joining of the system with only n coordinate factors. For n ≥ 2 we show that, whenever the maximal spectral type of a weakly mixing automorphism T is singular with respect to the convolution of any n continuous measures, i.e. T has the so-called convolution singularity property of order n,...
Dispersing cocycles and mixing flows under functions
Let T be a measure-preserving and mixing action of a countable abelian group G on a probability space (X,,μ) and A a locally compact second countable abelian group. A cocycle c: G × X → A for T disperses if in measure for every map α: G → A. We prove that such a cocycle c does not disperse if and only if there exists a compact subgroup A₀ ⊂ A such that the composition θ ∘ c: G × X → A/A₀ of c with the quotient map θ: A → A/A₀ is trivial (i.e. cohomologous to a homomorphism η: G → A/A₀). This result...
Dispersion properties of ergodic translations.
Dispersionless Hirota equations of two-component BKP hierarchy.
Disques de Siegel et anneaux de Herman
Dissipation Induced Instabilities
Dissipative dynamics of reaction diffusion equations in
Dissipative initial boundary value problem for the BBM-equation.
Dissipative Systems on Manifolds.
Distal actions and ergodic actions on compact groups.
Distortion bounds for unimodal maps
We obtain estimates for derivative and cross-ratio distortion for (any η > 0) unimodal maps with non-flat critical points. We do not require any “Schwarzian-like” condition. For two intervals J ⊂ T, the cross-ratio is defined as the value B(T,J): = (|T| |J|)/(|L| |R|) where L,R are the left and right connected components of T∖J respectively. For an interval map g such that is a diffeomorphism, we consider the cross-ratio distortion to be B(g,T,J): = B(g(T),g(J))/B(T,J). We prove that for...
Distortion in transformation groups (with an appendix by Yves de Cornulier).
Distortion inequality for the Frobenius-Perron operator and some of its consequences in ergodic theory of Markov maps in
Asymptotic properties of the sequences (a) and (b) , where is the Frobenius-Perron operator associated with a nonsingular Markov map defined on a σ-finite measure space, are studied for g ∈ G = f ∈ L¹: f ≥ 0 and ⃦f ⃦ = 1. An operator-theoretic analogue of Rényi’s Condition is introduced. It is proved that under some additional assumptions this condition implies the L¹-convergence of the sequences (a) and (b) to a unique g₀ ∈ G. The general result is applied to some smooth Markov maps in ....