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 , like the piecewise linear sawtooth function. Its behavior is sometimes similar to the standard map, but considerably different in some cases.[more]
This map is related to outer billiards; other applications include digital filters .[less]
The sawtooth function is defined as
and the map is
where is a constant between 0 and 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.
 G. Hughes, "Outer Billiards, Digital Filters and Kicked Hamiltonians." arxiv.org/abs/1206.5223.