Titlebook: Construction of Mappings for Hamiltonian Systems and Their Applications; Sadrilla S. Abdullaev Book 2006 Springer-Verlag Berlin Heidelberg

商业上

Die Gewissheit unsicherer Zeitenperturbation of the integrable system. To study perturbed systems special theoretical methods, known as ., have been developed. They are based on the assumption that the solutions of a perturbed system are close to the corresponding solutions of the unperturbed (integrable) system, and one seeks the

hermitage

Die Gewissheit unsicherer Zeiten preface mappings significantly simplify the study of systems, by reducing the dimension of the system by one, visualizing the orbits on certain sections of phase space, and thus simplifying the formulation of many concepts of dynamical systems. In this chapter we review the traditional methods to c

Affectation

Die Gewissheit unsicherer Zeitensystems affected by perturbations. The method is based on the Hamilton–Jacobi method for integrating Hamiltonian equations and Jacobi’s theorem recalled in Sect. 1.2.2. As we have seen there the idea of the Hamilton–Jacobi method consists of finding such a canonical change of variables which reduces

越自我

https://doi.org/10.1007/978-3-531-92140-2any small time-periodic perturbation splits the separatrices corresponding to stable and unstable manifolds which leads to the onset of chaotic motion due to the exponential divergence of orbits with close initial conditions. This phenomenon creates the zone of phase space in the small vicinity of t

NATAL

https://doi.org/10.1007/978-3-531-92140-2clude a motion in a double–well potential, dynamics of the periodicallydriven oscillator. We consider also the dynamics of particles near the separatrix of long–range potential field. These problems are a motion of particle in a periodically–driven Morse potential and the Kepler problem.

anthropologist

Klaus-Ove Kahrmann,Peter Bendixeniltonian systems in which a so-called . is violated. Particular example of these system is a one–degree-of-freedom system with a non-monotonic dependence of the frequency of oscillations on action variable. The second problem is a study of systems subjected to non-smooth perturbations. These problem

Aerate

Klaus-Ove Kahrmann,Peter Bendixen It forms a stochastic layer, a zone, of chaotically unstable motion near the unperturbed separatrix. In this section we study important properties of the stochastic layer, namely, a rescaling invariance of phase space of systems near the saddle points. This property of motion is generic for typical

持续

Ungleiche Netzwerke - Vernetzte Ungleichheitdevices in a quest for the controlled fusion.. Actually, a fusion research in early sixties gave a huge impact on the development of Hamiltonian dynamics, particularly, on mapping methods. Since, particles predominantly follow magnetic field lines the determination of their structure is important to

缝纫

Ungleiche Netzwerke - Vernetzte Ungleichheitic field lines in so-called ergodic and poloidal divertor tokamaks using mappings. We shall study the general structure of magnetic field, chaotic and statistical properties of field lines in ergodic divertor tokamaks. Mappings constitute an important and computationally efficient tool to study magn

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