Normalizations with Exponentially Small Remainders for Nonautonomous Analytic Periodic Vector Fields

Normal Forms of Analytic Perturbations of Quasihomogeneous Vector Fields: Rigidity, Invariant Analytic Sets and Exponentially Small Approximation

construction of vector fields with positive lyapunov exponents

in this thesis our aim is to construct vector field in r3 for which the corresponding one-dimensional maps have certain discontinuities. two kinds of vector fields are considered, the first the lorenz vector field, and the second originally introced here. the latter have chaotic behavior and motivate a class of one-parameter families of maps which have positive lyapunov exponents for an open in...

Exponentially Long Time Stability near an Equilibrium Point for Non–linearizable Analytic Vector Fields

We study the orbit behavior of a germ of an analytic vector field of (C, 0), n ≥ 2. We prove that if its linear part is semisimple, non–resonant and verifies a Bruno–like condition, then the origin is effectively stable: stable for finite but exponentially long times.

Exponentially Localized Wannier Functions in Periodic Zero Flux Magnetic Fields

Integrable Analytic Vector Fields with a Nilpotent Linear Part

We study the normalization of integrable analytic vector fields with a nilpotent linear part. We prove that such an analytic vector field can be transformed into a certain form by convergent transformations when it has a non-singular formal integral. In particular, we show that a formally linearizable analytic vector field with a nilpotent linear part is linearizable by convergent transformatio...