Elastic Problems and Optimal Control: Integrable Systems
Electromagnetic dynamical systems.
Elementary examples of Loewner chains generated by densities
We study explicit examples of Loewner chains generated by absolutely continuous driving measures, and discuss how properties of driving measures are reflected in the shapes of the growing Loewner hulls.
Éléments de distorsion de
Dans cet article, on montre que, dans le groupe des difféomorphismes isotopes à l’identité d’une variété compacte , tout élément récurrent est de distorsion. Pour ce faire, on généralise une méthode de démonstration utilisée par Avila pour le cas de . La méthode nous permet de retrouver un résultat de Calegari et Freedman selon lequel tout homéomorphisme de la sphère isotope à l’identité est un élément de distorsion.
Elements of a qualitative theory of Hamiltonian PDEs.
Elliptic K3 surfaces as dynamical models and their Hamiltonian monodromy
This note deals with Lagrangian fibrations of elliptic K3 surfaces and the associated Hamiltonian monodromy. The fibration is constructed through the Weierstraß normal form of elliptic surfaces. There is given an example of K3 dynamical models with the identity monodromy matrix around 12 elementary singular loci.
Ellis groups of quasi-factors of minimal flows
A quasi-factor of a minimal flow is a minimal subset of the induced flow on the space of closed subsets. We study a particular kind of quasi-factor (a 'joining' quasi-factor) using the Galois theory of minimal flows. We also investigate the relation between factors and quasi-factors.
Embedding inverse limits interval maps as attractors
Embedding inverse limits of nearly Markov interval maps as attracting sets of planar diffeomorphisms
In this paper we address the following question due to Marcy Barge: For what f:I → I is it the case that the inverse limit of I with single bonding map f can be embedded in the plane so that the shift homeomorphism extends to a diffeomorphism ([BB, Problem 1.5], [BK, Problem 3])? This question could also be phrased as follows: Given a map f:I → I, find a diffeomorphism so that F restricted to its full attracting set, , is topologically conjugate to . In this situation, we say that the inverse...
Embedding odometers in cellular automata
We consider the problem of embedding odometers in one-dimensional cellular automata. We show that (1) every odometer can be embedded in a gliders-with-reflecting-walls cellular automaton, which one depending on the odometer, and (2) an odometer can be embedded in a cellular automaton with local rule (i ∈ ℤ), where n depends on the odometer, if and only if it is “finitary.”
Embedding solenoids
A generalized solenoid is an inverse limit space with bonding maps that are (regular) covering maps of closed compact manifolds. We study the embedding properties of solenoids in linear space and in foliations.
Embedding tiling spaces in surfaces
We show that an aperiodic minimal tiling space with only finitely many asymptotic composants embeds in a surface if and only if it is the suspension of a symbolic interval exchange transformation (possibly with reversals). We give two necessary conditions for an aperiodic primitive substitution tiling space to embed in a surface. In the case of substitutions on two symbols our classification is nearly complete. The results characterize the codimension one hyperbolic attractors of surface diffeomorphisms...
Endogenous instability in credit-constrained emerging economies with Leontief technology.
Endomorphic actions of ßN on the torus group.
Endomorphisms of symbolic algebraic varieties
The theorem of Ax says that any regular selfmapping of a complex algebraic variety is either surjective or non-injective; this property is called surjunctivity and investigated in the present paper in the category of proregular mappings of proalgebraic spaces. We show that such maps are surjunctive if they commute with sufficiently large automorphism groups. Of particular interest is the case of proalgebraic varieties over infinite graphs. The paper intends to bring out relations between model theory,...
Endomorphisms of the Cuntz algebras
This mainly expository article is devoted to recent advances in the study of dynamical aspects of the Cuntz algebras 𝓞ₙ, n < ∞, via their automorphisms and, more generally, endomorphisms. A combinatorial description of permutative automorphisms of 𝓞ₙ in terms of labelled, rooted trees is presented. This in turn gives rise to an algebraic characterization of the restricted Weyl group of 𝓞ₙ. It is shown how this group is related to certain classical dynamical systems on the Cantor set. An identification...
Energy-preserving Runge-Kutta methods
We show that while Runge-Kutta methods cannot preserve polynomial invariants in general, they can preserve polynomials that are the energy invariant of canonical Hamiltonian systems.
Engouffrement symplectique et intersections lagrangiennes.
Enhanced cryptography by multiple chaotic dynamics.
Ensemble oscillant d’un homéomorphisme de Brouwer, homéomorphismes de Reeb
Un homéomorphisme de Brouwer est un homéomorphisme du plan, sans point fixe, préservant l’orientation. Le théorème des translations planes affirme qu’un tel homéomorphisme s’obtient toujours en « recollant des translations ». Dans cet article, nous introduisons un nouvel invariant de conjugaison des homéomorphismes de Brouwer, l’ensemble oscillant, pour tenter de décrire assez précisément la manière dont s’effectue le recollement des translations. D’une part, nous utilisons la notion d’ensemble...