Linear mod one transformations and the distribution of fractional parts {ξ(p/q)ⁿ}
Linear programming interpretations of Mather’s variational principle
We discuss some implications of linear programming for Mather theory [13, 14, 15] and its finite dimensional approximations. We find that the complementary slackness condition of duality theory formally implies that the Mather set lies in an -dimensional graph and as well predicts the relevant nonlinear PDE for the “weak KAM” theory of Fathi [6, 7, 8, 5].
Linear programming interpretations of Mather's variational principle
We discuss some implications of linear programming for Mather theory [13-15] and its finite dimensional approximations. We find that the complementary slackness condition of duality theory formally implies that the Mather set lies in an n-dimensional graph and as well predicts the relevant nonlinear PDE for the “weak KAM” theory of Fathi [5-8].
Linear response for smooth deformations of generic nonuniformly hyperbolic unimodal maps
We consider families of unimodal maps whose critical point is slowly recurrent, and we show that the unique absolutely continuous invariant measure of depends differentiably on , as a distribution of order . The proof uses transfer operators on towers whose level boundaries are mollified via smooth cutoff functions, in order to avoid artificial discontinuities. We give a new representation of for a Benedicks-Carleson map , in terms of a single smooth function and the inverse branches...
Linéarisation de certaines structures de Poisson de classe
Linéarisation des perturbations holomorphes des rotations et applications
Linearisierung formal-biholomorpher Abbildungen und Interationsprobleme.
Linearising two-dimensional integrable systems and the construction of action-angle variables.
Linearizability of a polynomial system
Linearization of analytic and non-analytic germs of diffeomorphisms of
Linearization of germs: regular dependence on the multiplier
We prove that the linearization of a germ of holomorphic map of the type has a -holomorphic dependence on the multiplier . -holomorphic functions are -Whitney smooth functions, defined on compact subsets and which belong to the kernel of the operator. The linearization is analytic for and the unit circle appears as a natural boundary (because of resonances,i.e.roots of unity). However the linearization is still defined at most points of , namely those points which lie “far enough from...
Linearization of nonholonomic systems at equilibrium points.
Linearization of Normally Hyperbolic Diffeomorphisms and Flows
Linearization of Poisson actions and singular values of matrix products
We prove that the linearization functor from the category of Hamiltonian -actions with group-valued moment maps in the sense of Lu, to the category of ordinary Hamiltonian - actions, preserves products up to symplectic isomorphism. As an application, we give a new proof of the Thompson conjecture on singular values of matrix products and extend this result to the case of real matrices. We give a formula for the Liouville volume of these spaces and obtain from it a hyperbolic version of the Duflo...
Linearized geometric dynamics of Tobin-Benhabib-Miyao economic flow.
Links of homeomorphisms of a disk and topological entropy.
Liouville integrability of geometric variational problems.
Lissajous knots and billiard knots
We show that Lissajous knots are equivalent to billiard knots in a cube. We consider also knots in general 3-dimensional billiard tables. We analyse symmetry of knots in billiard tables and show in particular that the Alexander polynomial of a Lissajous knot is a square modulo 2.
Li-Yorke pairs of full Hausdorff dimension for some chaotic dynamical systems
We show that for some simple classical chaotic dynamical systems the set of Li-Yorke pairs has full Hausdorff dimension on invariant sets.
Ljusternik-Schnirelman theory with local Palais-Smale condition and singular dynamical systems