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pro vyhledávání: '"Delshams, A."'
We consider the Rydberg electron in a circularly polarized microwave field, whose dynamics is described by a 2 d.o.f. Hamiltonian, which is a perturbation of size $K>0$ of the standard rotating Kepler problem. In a rotating frame, the largest chaotic
Externí odkaz:
http://arxiv.org/abs/2411.10407
Autor:
Delshams, Amadeu, Zgliczynski, Piotr
In this work we consider a saddle-center equilibrium for general vector fields as well as Hamiltonian systems, and we transform it locally into a polynomial normal form in the saddle variables by a change of coordinates. This problem was first solved
Externí odkaz:
http://arxiv.org/abs/2411.04600
Autor:
Delshams, Amadeu, Zgliczynski, Piotr
We deal with dynamical systems on complex lattices possessing chains of non-transversal heteroclinic connections between several periodic orbits. The systems we consider are inspired by the so-called \emph{toy model systems} (TMS) used to prove the e
Externí odkaz:
http://arxiv.org/abs/2406.00398
In the present paper we apply the geometrical mechanism of diffusion in an \emph{a priori} unstable Hamiltonian system with 3 $+$ 1/2 degrees of freedom. This mechanism consists of combining iterations of the \emph{inner} and \emph{outer} dynamics as
Externí odkaz:
http://arxiv.org/abs/2310.18787
Exponentially small splitting of separatrices associated to 3D whiskered tori with cubic frequencies
We study the splitting of invariant manifolds of whiskered (hyperbolic) tori with three frequencies in a nearly-integrable Hamiltonian system, whose hyperbolic part is given by a pendulum. We consider a 3-dimensional torus with a fast frequency vecto
Externí odkaz:
http://arxiv.org/abs/1906.01439
We consider heteroclinic attractor networks motivated by models of competition between neural populations during binocular rivalry. We show that Gamma distributions of dominance times observed experimentally in binocular rivalry and other forms of bi
Externí odkaz:
http://arxiv.org/abs/1809.05860
Autor:
Delshams, Amadeu, Schaefer, Rodrigo G.
We prove that for any non-trivial perturbation depending on any two independent harmonics of a pendulum and a rotor there is global instability. The proof is based on the geometrical method and relies on the concrete computation of several scattering
Externí odkaz:
http://arxiv.org/abs/1710.00029
Publikováno v:
Int. J. Geom. Methods Mod. Phys. 16 (2019), suppl. 1, 1940008, 16 pp
In this paper we analyze in detail a collection of motivating examples to consider $b^m$-symplectic forms and folded-type symplectic structures. In particular, we provide models in Celestial Mechanics for every $b^m$-symplectic structure. At the end
Externí odkaz:
http://arxiv.org/abs/1705.03846
We present a new result about the shadowing of nontransversal chain of heteroclinic connections based on the idea of dropping dimensions. We illustrate this new mechanism with several examples. As an application we discuss this mechanism in a simplif
Externí odkaz:
http://arxiv.org/abs/1701.08193
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