Tangencies for real and complex Hénon maps: An analytic method.
Tauberian theorems for vector-valued Fourier and Laplace transforms
Let X be a Banach space and be absolutely regular (i.e. integrable when divided by some polynomial). If the distributional Fourier transform of f is locally integrable then f converges to 0 at infinity in some sense to be made precise. From this result we deduce some Tauberian theorems for Fourier and Laplace transforms, which can be improved if the underlying Banach space has the analytic Radon-Nikodym property.
The set of recurrent points of a continuous self-map on compact metric spaces and strong chaos
We discuss the existence of an uncountable strongly chaotic set of a continuous self-map on a compact metric space. It is proved that if a continuous self-map on a compact metric space has a regular shift invariant set then it has an uncountable strongly chaotic set in which each point is recurrent, but is not almost periodic.
Topological entropy and differential equations
On the background of a brief survey panorama of results on the topic in the title, one new theorem is presented concerning a positive topological entropy (i.e. topological chaos) for the impulsive differential equations on the Cartesian product of compact intervals, which is positively invariant under the composition of the associated Poincaré translation operator with a multivalued upper semicontinuous impulsive mapping.
Trajectory sensitivity method and master-slave synchronization to estimate parameters of nonlinear systems.
Trichotomy and bounded solutions of nonlinear differential equations
The existence of bounded solutions for equations in Banach spaces is proved. We assume that the linear part is trichotomic and the perturbation satisfies some conditions expressed in terms of measures of noncompactness.