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The Sawtooth Standard Map

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The standard map is studied in the context of Hamiltonian chaos, but other forms of the kick function have been introduced [1], like the piecewise linear sawtooth function. Its behavior is sometimes similar to the standard map, but considerably different in some cases.

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This map is related to outer billiards; other applications include digital filters [2].

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Contributed by: Enrique Zeleny (March 2013)
Open content licensed under CC BY-NC-SA

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Details

The sawtooth function is defined as

and the map is

,

where is a constant between 0 and 1.

References

[1] P. Ashwin, "Elliptic Behaviour in the Sawtooth Standard Map," Physics Letters A, 232(6), 1997 pp. 409–416. doi:10.1016/S0375-9601(97)00455-6.

[2] G. Hughes, "Outer Billiards, Digital Filters and Kicked Hamiltonians." arxiv.org/abs/1206.5223.

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