The Sawtooth Standard Map

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


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The sawtooth function is defined as
and the map is
where is a constant between 0 and 1.
[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."
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