Related papers: Dense heteroclinic tangencies near a Bykov cycle

The crossing of a transition state in a multidimensional reactive system is mediated by invariant geometric objects in phase space: An invariant hyper-sphere that represents the transition state itself and invariant hyper-cylinders that…

Takens Theorem for a partially hyperbolic dynamics provides a normal linearization along the center manifold. In this paper, we give the nonautonomous version of Takens Theorem under non-resonance conditions formulated in terms of the…

We elucidate the escape properties of stars moving in the combined gravitational field of a binary system of two interacting dwarf spheroidal galaxies. A galaxy model of three degrees of freedom is adopted for describing the dynamical…

We consider the dynamics of vector fields on three-manifolds which are constrained to lie within a plane field, such as occurs in nonholonomic dynamics. On compact manifolds, such vector fields force dynamics beyond that of a gradient flow,…

This paper extends sliding-mode control theory to nonlinear systems evolving on smooth manifolds. Building on differential geometric methods, we reformulate Filippov's notion of solutions, characterize well-defined vector fields on quotient…

We show, using covariant Lyapunov vectors, that the tangent space of spatially-extended dissipative systems is split into two hyperbolically decoupled subspaces: one comprising a finite number of frequently entangled "physical" modes, which…

In this paper new numerical invariants of structurally unstable vector fields in the plane are found. One of the main tools is an improved asymptotics of sparkling saddle connections that occur when a separatrix loop of a hyperbolic saddle…

The dynamics of many important high-dimensional dynamical systems are both chaotic and complex, meaning that strong reducing hypotheses are required to understand the dynamics. The highly influential chaotic hypothesis of Gallavotti and…

An analytic reversible Hamiltonian system with two degrees of freedom is studied in a neighborhood of its symmetric heteroclinic connection made up of a symmetric saddle-center, a symmetric orientable saddle periodic orbit lying in the same…

In a neighborhood of a hyperbolic periodic orbit of a volume-preserving flow on a manifold of dimension 3, we define and show the existence of a normal form for the generator of the flow that encodes the dynamics. If the flow is a contact…

In this paper, we construct (a) a pair of two regular Cantor sets in higher dimension which exhibits $C^1$-stable intersection and (b) a hyperbolic basic set which exhibits $C^2$-robust homoclinic tangency of the largest codimension for any…

We show the existence of a family of manifolds on which all (pointwise or absolutely) partially hyperbolic systems are dynamically coherent. This family is the set of 3-manifolds with nilpotent, non-abelian fundamental group. We further…

We construct pairs of non-isometric hyperbolic 3-orbifolds with the same topological type and volume. Topologically these orbifolds are mapping tori of pseudo-Anosov maps of the surface of genus 2, with singular locus a fibred (hyperbolic)…

This article studies routes to chaos occurring within a resonance wedge for a 3-parametric family of differential equations acting on a 3-sphere. Our starting point is an autonomous vector field whose flow exhibits a weakly attracting…

We consider compact sets which are invariant and partially hyperbolic under the dynamics of a diffeomorphism of a manifold. We prove that such a set K is contained in a locally invariant center submanifold if and only if each strong stable…

We review the theory of strange attractors and their bifurcations. All known strange attractors may be subdivided into the following three groups: hyperbolic, pseudo-hyperbolic ones and quasi-attractors. For the first ones the description…

We consider an integrable Hamiltonian system weakly coupled with a pendulum-type system. For each energy level within some range, the uncoupled system is assumed to possess a normally hyperbolic invariant manifold diffeomorphic to a…

We develop a Melnikov method for volume-preserving maps with codimension one invariant manifolds. The Melnikov function is shown to be related to the flux of the perturbation through the unperturbed invariant surface. As an example, we…

In two-dimensional unfoldings of homoclinic tangencies, the parameter space contains codimension one laminations whose leaves consist of maps with invariant non-hyperbolic Cantor sets. These Cantor sets are wild both in the sense of…

In this paper we express the Minkowski dimension of spiral trajectories near hyperbolic saddles and semi-hyperbolic singularities in terms of the Minkowski dimension of intersections of such spirals with transversals near these…