相关论文: Heteroclinic intersections between Invariant Circl…
We study bifurcations of non-orientable area-preserving maps with quadratic homoclinic tangencies. We study the case when the maps are given on non-orientable two-dimensional surfaces. We consider one and two parameter general unfoldings…
In this paper we study a beyond all order phenomenon which appears in the analytic unfoldings of the Hopf-zero singularity. It consists in the breakdown of a two-dimensional heteroclinic surface which exists in the truncated normal form of…
In this work the Melnikov method for perturbed Hamiltonian wave equations is considered in order to determine possible chaotic behaviour in the systems. The backbone of the analysis is the multi-symplectic formulation of the unperturbed PDE…
We study bifurcations of area-preserving maps, both orientable (symplectic) and non-orientable, with quadratic homoclinic tangencies. We consider one and two parameter general unfoldings and establish results related to the appearance of…
We present a methodology for computer assisted proofs of Shil'nikov homoclinic intersections. It is based on geometric bounds on the invariant manifolds using rate conditions, and on propagating the bounds by an interval arithmetic…
We use Busemann functions to construct volume preserving mappings in an asymptotically harmonic manifold. If the asymptotically harmonic manifold satisfies the visibility condition, we construct mappings which preserve distances in some…
Topological techniques are powerful tools for characterizing the complexity of many dynamical systems, including the commonly studied area-preserving maps of the plane. However, the extension of many topological techniques to higher…
We show the existence of Shilnikov-type dynamics and bifurcation behaviour in general discrete three-dimensional piecewise smooth maps and give analytical results for the occurence of such dynamical behaviour. Our main example in fact shows…
The Melnikov criterion is used to examine a global homoclinic bifurcation and transition to chaos in the case of a quarter car model excited kinematically by the road surface profile. By analyzing the potential an analytic expression is…
We consider a mechanical system consisting of $n$ penduli and a $d$-dimensional generalized rotator subject to a time-dependent perturbation. The perturbation is not assumed to be either Hamiltonian, or periodic or quasi-periodic. The…
In this work we develop a method for computing mathematically rigorous enclosures of some one dimensional manifolds of heteroclinic orbits for nonlinear maps. Our method exploits a rigorous curve following argument build on high order…
Stable and unstable manifolds, originating from hyperbolic cycles, fundamentally characterize the behaviour of dynamical systems in chaotic regions. This letter demonstrates that their shifts under perturbation, crucial for chaos control,…
A class of n-dimensional Poisson systems reducible to an unperturbed harmonic oscillator shall be considered. In such case, perturbations leaving invariant a given symplectic leaf shall be investigated. Our purpose will be to analyze the…
Recent studies suggest that unstable recurrent solutions of the Navier-Stokes equation provide new insights into dynamics of turbulent flows. In this study, we compute an extensive network of dynamical connections between such solutions in…
We study the flux homomorphism for closed forms of arbitrary degree, with special emphasis on volume forms and on symplectic forms. The volume flux group is an invariant of the underlying manifold, whose non-vanishing implies that the…
We consider closed and orientable immersed hypersurfaces of translational manifolds. Given a vector field on such a hypersurface, we define a perturbation of its Gauss map, which allows us to obtain topological invariants for the immersion…
A long-standing question is what invariant sets can be shared by two maps acting on the same space. A similar question stands for invariant measures. A particular interesting case are expanding Markov maps of the circle. If the two involved…
Heterodimensional cycles are heteroclinic cycles that connect periodic orbits whose unstable manifolds have different dimensions. This is a source of nonhyperbolic dynamics and unstable dimension variability. For smooth invertible maps…
We study the effect of time-dependent, non-conservative perturbations on the dynamics along homoclinic orbits to a normally hyperbolic invariant manifold. We assume that the unperturbed system is Hamiltonian, and the normally hyperbolic…
Let $M$ be a closed manifold. Polterovich constructed a linear map from the vector space of quasi-morphisms on the fundamental group $\pi _{1}(M)$ of $M$ to the space of quasi-morphisms on the identity component ${\rm…