A Γ-convergence result for variational integrators of lagrangians with quadratic growth
Following the Γ-convergence approach introduced by Müller and Ortiz, the convergence of discrete dynamics for Lagrangians with quadratic behavior is established.
Abelian Cocycles for Nonsingular Ergodic Transformations and the Genericity of Type III... Transformations.
Abelian groups of zero adjoint entropy
The notion of adjoint entropy for endomorphisms of an Abelian group is somehow dual to that of algebraic entropy. The Abelian groups of zero adjoint entropy, i.e. ones whose endomorphisms all have zero adjoint entropy, are investigated. Torsion groups and cotorsion groups satisfying this condition are characterized. It is shown that many classes of torsionfree groups contain groups of either zero or infinite adjoint entropy. In particular, no characterization of torsionfree groups of zero adjoint...
Abelian integrals for quadratic vector fields.
Abelian integrals in holomorphic foliations.
The aim of this paper is to introduce the theory of Abelian integrals for holomorphic foliations in a complex manifold of dimension two. We will show the importance of Picard-Lefschetz theory and the classification of relatively exact 1-forms in this theory. As an application we identify some irreducible components of the space of holomorphic foliations of a fixed degree and with a center singularity in the projective space of dimension two. Also we calculate higher Melnikov functions under some...
Abelian integrals of quadratic Hamiltonian vector fields with an invariant straight line.
We prove that the lowest upper bound for the number of isolated zeros of the Abelian integrals associated to quadratic Hamiltonian vector fields having a center and an invariant straight line after quadratic perturbations is one.
Abelian integrals related to Morse polynomials and perturbations of plane hamiltonian vector fields
Let be the real vector space of Abelian integralswhere is a fixed real polynomial, is an arbitrary real polynomial and , , is the interior of the oval of which surrounds the origin and tends to it as . We prove that if is a semiweighted homogeneous polynomial with only Morse critical points, then is a free finitely generated module over the ring of real polynomials , and compute its rank. We find the generators of in the case when is an arbitrary cubic polynomial. Finally we...
Abelian surfaces and Kowalewski's top
Abelian varieties, surfaces of general type and integrable systems.
About boundary terms in higher order theories
It is shown that when in a higher order variational principle one fixes fields at the boundary leaving the field derivatives unconstrained, then the variational principle (in particular the solution space) is not invariant with respect to the addition of boundary terms to the action, as it happens instead when the correct procedure is applied. Examples are considered to show how leaving derivatives of fields unconstrained affects the physical interpretation of the model. This is justified in particular...
About chaotization mechanisms of the distributed dynamical systems which are close to discrete.
About projections of logarithmic Sobolev inequalities
About some theorems by L. P. Šil'nikov
About Stefan's definition of a foliation with singularities : a reduction of the axioms
About the Algebraic Yuzvinski Formula
The Algebraic Yuzvinski Formula expresses the algebraic entropy of an endomorphism of a finitedimensional rational vector space as the Mahler measure of its characteristic polynomial. In a recent paper, we have proved this formula, independently fromits counterpart – the Yuzvinski Formula – for the topological entropy proved by Yuzvinski in 1968. In this paper we first compare the proof of the Algebraic Yuzvinski Formula with a proof of the Yuzvinski Formula given by Lind and Ward in 1988, underlying...
About the attractive points of the root functions on the Riemannian foliation.
About the existence of the thermodynamic limit for some deterministic sequences of the unit circle.
About the existence of the thermodynamic limit for some deterministic sequences of the unit circle.
Absolute continuity, Lyapunov exponents and rigidity I: geodesic flows
We consider volume-preserving perturbations of the time-one map of the geodesic flow of a compact surface with negative curvature. We show that if the Liouville measure has Lebesgue disintegration along the center foliation then the perturbation is itself the time-one map of a smooth volume-preserving flow, and that otherwise the disintegration is necessarily atomic.
Absolute Stability and Bifurcation Theory.