Standard Map on a Torus - Maple Application Center
Application Center Applications Standard Map on a Torus

Standard Map on a Torus

: Frank Wang
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Maple worksheet for producing a standard map on a torus is developed. A brief introduction of Hamiltonian mechanics using a simple pendulum system as an example is provided, followed by a discussion of a kicked rotor system which consists of a simple pendulum with the potential energy turned on in delta-function pulses. The integration of the kicked rotor problem yields the standard map, which has characteristics of a large class of systems. Plotting the standard map on a torus facilitates a three-dimensional visualization the Kolmogorov-Arnold-Moser (KAM) theory of chaos in a Hamiltonian system. An animation demonstrating chaos created by homoclinic tangle near a hyperbolic point is contained in this worksheet.

Application Details

Publish Date: January 10, 2006
Created In: Maple 10
Language: English

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