File:An Arnold standard map with two attractors of period 4.png
Original file (1,920 × 1,080 pixels, file size: 2.04 MB, MIME type: image/png)
Captions
Captions
Summary
[edit]
| Description |
English: This image shows the dynamical plane of (the complexification of) the circle map defined by f(x) = x + a + b*sin(2*pi(x))/(2*pi) (mod 1), where a=0.201 and b=2.864.
This is an element of the so-called Arnold family, also known as the standard family, of circle maps - the simplest mathematical model of phase-locking phenomena. The function in question has two periodic attractors of period 4; their basins are shown in purple and red. (The components of the second basin are very small.) Points that do not eventually enter the unit circle under iteration are shown in grey, with different shades depending on how often the orbit maps inside / outside of the circle. This image was used in the exhibit "Dynamical Systems and Chaos: The Arnold Family" at the IMA@50 Festival of Mathematics and its Applications in Manchester, July 2014, illustrating recent research by Rempe-Gillen and van Strien. |
| Date | |
| Source | Own work |
| Author | Lasse Rempe-Gillen |
Licensing
[edit]
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 10:10, 15 June 2015 | | 1,920 × 1,080 (2.04 MB) | Lasserempe (talk | contribs) | User created page with UploadWizard |
You cannot overwrite this file.
File usage on Commons
There are no pages that use this file.
File usage on other wikis
The following other wikis use this file:
- Usage on en.wikipedia.org
