The Sawtooth Standard Map

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

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.

[more]

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

[less]

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


Snapshots


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.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send