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SIAM Journal on Mathematical Analysis, 1984
Scaling techniques are very important and powerful means to simplify dynamical problems. In this clearly written survey paper a detailed discussion of scaling of variables for Hamiltonian systems is presented by introducing a series of examples of increasing complexity.
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Scaling techniques are very important and powerful means to simplify dynamical problems. In this clearly written survey paper a detailed discussion of scaling of variables for Hamiltonian systems is presented by introducing a series of examples of increasing complexity.
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Hamiltonian Systems with Convex Hamiltonians
2004A well-known theorem states that if a level surface of a Hamiltonian is convex, then it contains a periodic trajectory of the Hamiltonian system [142], [147]. In this chapter we prove a more general statement as an application of optimal control theory for linear systems.
Andrei A. Agrachev, Yuri L. Sachkov
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2000
Abstract When a system involves no dissipative mechanisms such as friction, we say that the system is conservative because its total energy is conserved and the behaviour is described by a time-independent Hamiltonian function. In that case, the notion of attractor no longer applies. Different initial conditions (starting points in state
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Abstract When a system involves no dissipative mechanisms such as friction, we say that the system is conservative because its total energy is conserved and the behaviour is described by a time-independent Hamiltonian function. In that case, the notion of attractor no longer applies. Different initial conditions (starting points in state
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Dynamical systems that are amenable to formulation in terms of a Hamiltonian function or operator encompass a vast swath of fundamental cases in applied mathematics and physics. This carefully edited volume represents work carried out during the special program on Hamiltonian Systems at MSRI in the Fall of 2018.
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1989
This introduction to the theory of Hamiltonian chaos outlines the main results in the field, and goes on to consider implications for quantum mechanics. The study of nonlinear dynamics, and in particular of chaotic systems, is one of the fastest growing and most productive areas in physics and applied mathematics. In its first six chapters, this timely
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This introduction to the theory of Hamiltonian chaos outlines the main results in the field, and goes on to consider implications for quantum mechanics. The study of nonlinear dynamics, and in particular of chaotic systems, is one of the fastest growing and most productive areas in physics and applied mathematics. In its first six chapters, this timely
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