منابع مشابه
Hamiltonian structure of hamiltonian chaos
From a kinematical point of view, the geometrical information of hamiltonian chaos is given by the (un)stable directions, while the dynamical information is given by the Lyapunov exponents. The finite time Lyapunov exponents are of particular importance in physics. The spatial variations of the finite time Lyapunov exponent and its associated (un)stable direction are related. Both of them are f...
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für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License. Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namen...
متن کاملHamiltonian Systems and Chaos Overview
In this paper we will give an overview of Hamiltonian systems with specific examples, including the classical pendulum example. Upon addressing the properties of Hamiltonian systems we will then explore how chaos arises. More specifically, we will consider two examples: solar system orbits and a zero-sum two-player game.
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Hamiltonian systems with two or more degrees of freedom are generally nonintegrable which usually involves chaotic dynamics. The size of the chaotic sets determines for a large part the nature and influence of chaos. Near stable equilibrium we can obtain normal forms that often produce ‘formal integrability’ of the Hamiltonian system and at the same time produce rigorous but not necessarily opt...
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We show that Gutzwiller’s characterization of chaotic Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor in the structure of the Hamiltonian can be extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce the Hamilton equations of the original potential model when a transition i...
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ژورنال
عنوان ژورنال: Physics Letters A
سال: 1997
ISSN: 0375-9601
DOI: 10.1016/s0375-9601(97)00797-4