Affine spheres: Discretization via duality relations.
Affinor structures in the oscillation theory
In this paper we consider the system of Hamiltonian differential equations, which determines small oscillations of a dynamical system with n parameters. We demonstrate that this system determines an affinor structure J on the phase space TRⁿ. If J² = ωI, where ω = ±1,0, the phase space can be considered as the biplanar space of elliptic, hyperbolic or parabolic type. In the Euclidean case (Rⁿ = Eⁿ) we obtain the Hopf bundle and its analogs. The bases of these bundles are, respectively, the projective...
Algebraic and ergodic properties of a new continued fraction algorithm with non-decreasing partial quotients
In this paper the Engel continued fraction (ECF) expansion of any is introduced. Basic and ergodic properties of this expansion are studied. Also the relation between the ECF and F. Ryde’s monotonen, nicht-abnehmenden Kettenbruch (MNK) is studied.
Algebraic calculation of the energy eigenvalues for the nondegenerate three-dimensional Kepler-Coulomb potential.
Algebraic complete integrability of an integrable system of Beauville
We show that the Beauville’s integrable system on a ten dimensional moduli space of sheaves on a K3 surface constructed via a moduli space of stable sheaves on cubic threefolds is algebraically completely integrable, using O’Grady’s construction of a symplectic resolution of the moduli space of sheaves on a K3.
Algebraic degrees for iterates of meromorphic self-maps of Pk.
We first introduce the class of quasi-algebraically stable meromorphic maps of Pk. This class is strictly larger than that of algebraically stable meromorphic self-maps of Pk. Then we prove that all maps in the new class enjoy a recurrent property. In particular, the algebraic degrees for iterates of these maps can be computed and their first dynamical degrees are always algebraic integers.
Algebraic entropy for valuation domains
Let R be a non-discrete Archimedean valuation domain, G an R-module, Φ ∈ EndR(G).We compute the algebraic entropy entv(Φ), when Φ is restricted to a cyclic trajectory in G. We derive a special case of the Addition Theorem for entv, that is proved directly, without using the deep results and the difficult techniques of the paper by Salce and Virili [8].
Algebraic integrability of Schrodinger operators and representations of Lie algebras
Algebraic non-integrability of the Cohen map.
Algebraic periods of self-maps of a rational exterior space of rank 2.
Algebraic properties of the Lefschetz zeta function, periodic points and topological entropy.
The Lefschetz zeta function associated to a continuous self-map f of a compact manifold is a rational function P/Q. According to the parity of the degrees of the polynomials P and Q, we analyze when the set of periodic points of f is infinite and when the topological entropy is positive.
Algebraically completely integrable systems and Kummer varieties.
Algebras of integrals
Algèbres de Lie, systèmes hamiltoniens, courbes algébriques
Algèbres différentielles en théorie des champs
Les algèbres différentielles sont apparues comme des outils commodes ou même inévitables pour exprimer les symétries continues, exactes ou brisées, suivant la situation physique envisagée, dans le cadre de l’algorithme de Feynman de la théorie quantique des champs perturbative. Les algèbres de courants, les théories de Yang-Mills, la première quantification de la corde, sont proposées comme exemples classiques.
Algèbres et équations non-linéaires
Algebro-geometric Approach to the Yang-Baxter Equation and Related Topics
Algebro-geometric Integration in Classical and Statistical Mechanics
Algebro-geometric solutions of the Camassa-Holm hierarchy.
We provide a detailed treatment of the Camassa-Holm (CH) hierarchy with special emphasis on its algebro-geometric solutions. In analogy to other completely integrable hierarchies of soliton equations such as the KdV or AKNS hierarchies, the CH hierarchy is recursively constructed by means of a basic polynomial formalism invoking a spectral parameter. Moreover, we study Dubrovin-type equations for auxiliary divisors and associated trace formulas, consider the corresponding algebro-geometric initial...
All solenoids of piecewise smooth maps are period doubling
We show that piecewise smooth maps with a finite number of pieces of monotonicity and nowhere vanishing Lipschitz continuous derivative can have only period doubling solenoids. The proof is based on the fact that if is a periodic orbit of a continuous map f then there is a union set of some periodic orbits of f such that for any i.