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
Local analyticity in the time and space variables and the smoothing effect for the fifth-order KdV-type equation.
Local and global properties of nonautonomous dynamical systems and their application to competition models.
Local density of diffeomorphisms with large centralizers
Given any compact manifold , we construct a non-empty open subset of the space of -diffeomorphisms and a dense subset such that the centralizer of every diffeomorphism in is uncountable, hence non-trivial.
Local dimensions for Poincaré recurrences.
Local dynamics of holomorphic diffeomorphisms
This is a survey about local holomorphic dynamics, from Poincaré's times to nowadays. Some new ideas on how to relate discrete dynamics to continuous dynamics are also introduced. It is the text of the talk given by the author at the XVII UMI Congress at Milano.
Local Groups of Differentiable Transformations.
Local Lyapunov exponents and a local estimate of Hausdorff dimension