منابع مشابه
Measures of Chaos in Hamiltonian Systems
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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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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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...
متن کاملGeometric Interpretation of Chaos in Two-Dimensional Hamiltonian Systems
This paper exploits the fact that Hamiltonian flows associated with a time-independent H can be viewed as geodesic flows in a curved manifold, so that the problem of stability and the onset of chaos hinge on properties of the curvature Kab entering into the Jacobi equation. Attention focuses on ensembles of orbit segments evolved in representative twodimensional potentials, examining how such p...
متن کاملNonlinear Dynamics and Chaos in Many-Particle Hamiltonian Systems
We report the results of studies of nonlinear dynamics and dynamical chaos in Hamiltonian systems composed of many interacting particles. The importance of the Lyapunov exponents and the Kolmogorov-Sinai entropy is discussed in the context of ergodic theory and nonequilibrium statistical mechanics. Two types of systems are studied: hard-ball models for the motion of a tracer or Brownian particl...
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ژورنال
عنوان ژورنال: Celestial Mechanics and Dynamical Astronomy
سال: 2004
ISSN: 0923-2958,1572-9478
DOI: 10.1007/s10569-004-6445-3