We describe a method to establish existence and regularity of invariant manifolds and, at the
same time to find simple maps which are conjugated to the dynamics on them. The method …

… that DKy = Go e Cr~1 and hence Ky e Cr. The argument will be based on the following result.
… is convergent in Tr-i,Li> we conclude that DKy E rr_i,2._i C Cr_1 and hence that fC> e Cr. D …

… For g EE, and f E Ek with k 3 1 we introduce the linear operator &:… We will be particularly
concerned with the operator LH2: E, + Ek … First we analyze the effect of TX on an element of E,. …

… More generally, if ZC (Z+)2 is such that (i,j) SZ and ï < i, J < j implies (ï, J) GZ, we denote
by the set of functions / for which D\Dxf exists, is continuous and bounded for every (i,j) e Z …

… We extend E analytically to a neighbourhood of H^e(0,0) until il2 2 by using … analytically on
e we look for the initial condition z(e) of this orbit for t = r. It must satisfy that H"(z(e)) = z(e). For …

We present theorems which provide the existence of invariant whiskered tori in finite-dimensional
exact symplectic maps and flows. The method is based on the study of a functional …

We study the problem of exponentially small splitting of separatrices of one degree of freedom
classical Hamiltonian systems with a non-autonomous perturbation fast and periodic in …

We use the parameterization method to prove the existence and properties of one-dimensional
submanifolds of the center manifold associated to the fixed point of Cr maps with linear …

… Bottlenecking phenomena and its associated inverse square root scaling law have been
elegantly shown in an experiment with an electronic circuit modeling Duffing’s equation [20]. …

We consider differentiable maps having an invariant torus with normal behaviour and a central
part. We prove the existence and regularity of strong-stable manifolds and regularity with …