相关论文: Canonical Melnikov theory for diffeomorphisms

In this note the interrelations between several natural morphisms on the $\pi_1$ of groups of Hamiltonian diffeomorphisms are investigated. As an application, the equality of the (non-linear) Maslov index of loops of quantomorphisms of…

A heterodimensional cycle consists of a pair of heteroclinic connections between two saddle periodic orbits with unstable manifolds of different dimensions. Recent theoretical work on chaotic dynamics beyond the uniformly hyperbolic setting…

Initially motivated by Hrushovski's paper on definability patterns, we obtain homeomorphisms between Ellis semigroups related to natural actions of the automorphism groups of first order structures and certain collections of types and…

Let $F\in\mathbb{C}[x,y]$ be a polynomial, $\gamma(z)\in \pi_1(F^{-1}(z))$ a non-trivial cycle in a generic fiber of $F$ and let $\omega$ be a polynomial $1$-form, thus defining a polynomial deformation $dF+\epsilon\omega=0$ of the…

Let ($M$, $\Omega$) be a smooth symplectic manifold and $f:M\rightarrow M$ be a symplectic diffeomorphism of class $C^l$ ($l\geq 3$). Let $N$ be a compact submanifold of $M$ which is boundaryless and normally hyperbolic for $f$. We suppose…

We have studied a chaotic transport in a two-dimensional periodic vortical flow under a time-dependent perturbation with period T where the global diffusion occurs along the stochastic web. By using the Melnikov method we construct the…

We define a diffeology on the Milnor classifying space of a diffeological group $G$, constructed in a similar fashion to the topological version using an infinite join. Besides obtaining the expected classification theorem for smooth…

For the class of differentiable maps of the plane and, in particular, for standard-like maps (McMillan form), a simple relation is shown between the directions of the local invariant manifolds of a generic point and its contribution to the…

This paper deals with the problem of limit cycle bifurcations for piecewise smooth integrable differential systems with four zones. When the unperturbed system has a family of periodic orbits, the first order Melnikov function is derived…

A mechanical linkage is a mechanism made of rigid rods linked together by flexible joints, in which some vertices are fixed and others may move. The partial configuration space of a linkage is the set of all the possible positions of a…

The concept of sliding Shilnikov connection has been recently introduced and represents an important notion in Filippov systems, because its existence implies chaotic behavior on an invariant subset of the system. The investigation of its…

Given a Morse function f on a closed manifold M with distinct critical values, and given a field F, there is a canonical complex, called the Morse-Barannikov complex, which is equivalent to any Morse complex associated with f and whose form…

We make explicit the geometric content of Mel'nikov's method for detecting heteroclinic points between transversally hyperbolic periodic orbits. After developing the general theory of intersections for pairs of family of Lagrangian…

The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the…

We establish a Poincar\'e-Dulac theorem for sequences (G_n)_n of holomorphic contractions whose differentials d_0 G_n split regularly. The resonant relations determining the normal forms hold on the moduli of the exponential rates of…

We assign some kind of invariant manifolds to a given integrable PDE (its discrete or semi-discrete variant). First, we linearize the equation around its arbitrary solution $u$. Then we construct a differential (respectively, difference)…

We present and implement an algorithm for computing the invariant circle and the corresponding stable manifolds for 2-dimensional maps. The algorithm is based on the parameterization method, and it is backed up by an a-posteriori theorem…

We provide a rigorous construction of I.M. Singer's universal connection, a natural connection on a bundle of paths associated to any manifold, using the theory of diffeology. Furthermore, we generalize the universal connection to the…

We study the existence of periodic solutions in a class of planar Filippov systems obtained from non-autonomous periodic perturbations of reversible piecewise smooth differential systems. It is assumed that the unperturbed system presents a…

The first half of this paper is largely expository, wherein we present a systematic combinatorial approach to the theory of polynomial (semi)invariants and multilinear invariants of several vectors and covectors, for the classical groups.…