Ultradiscretization of solvable chaotic maps and the tropical geometry

44 mins 30 secs, 112.56 MB, WebM 450x360, 25.0 fps, 44100 Hz, 345.34 kbits/sec

Share this media item:

Embed this media item:

<iframe width="_width_" height="_height_" src="https://sms.cam.ac.uk/media/545004/embed" frameborder="0" scrolling="no" allowfullscreen></iframe>

Choose size:

About this item

Available Formats

About this item

Description:	Kajiwara, K (Kyushu) Thursday 02 April 2009, 11:30-12:15 Geometric Aspects of Discrete and Ultra-discrete Integrable Systems

Created:

2009-04-25 17:51

Collection:

Discrete Integrable Systems

Publisher:

Isaac Newton Institute

Kenji Kajiwara

Language:

eng (English)

Credits:

Author:	Kenji Kajiwara
Producer:	Jonathan Nimmo
Director:	Ehsan Ashraf
Editor:	Steve Greenham


Abstract:	A seminar from the Geometric Aspects of Discrete and Ultra-discrete Integrable Systems conference in association with the Newton Institute programme: Discrete Integrable Systems http://www.gla.ac.uk/departments/mathematics/research/isamp/events/gadudis/programme/ We consider a certain one-dimensional solvable chaotic map arising from the duplication formula of elliptic function, which is a generalization of the logistic map. Applying the ultradiscretization, we obtain the tent map and its general solution simultaneously. We then discuss the tropical geometric interpretation of the tent map; it arises from the duplication map of a certain tropical plane biquadratic curve. If time permits, I will mention on the map arising from the m-th multiplication formula of the elliptic function, and recent result on a certain two-dimensional map.

Abstract:

A seminar from the Geometric Aspects of Discrete and Ultra-discrete Integrable Systems conference in association with the Newton Institute programme: Discrete Integrable Systems

http://www.gla.ac.uk/departments/mathematics/research/isamp/events/gadudis/programme/

We consider a certain one-dimensional solvable chaotic map arising from the duplication formula of elliptic function, which is a generalization of the logistic map. Applying the ultradiscretization, we obtain the tent map and its general solution simultaneously. We then discuss the tropical geometric interpretation of the tent map; it arises from the duplication map of a certain tropical plane biquadratic curve. If time permits, I will mention on the map arising from the m-th multiplication formula of the elliptic function, and recent result on a certain two-dimensional map.

Available Formats

Format	Quality	Bitrate	Size
MPEG-4 Video	480x360	1.84 Mbits/sec	616.56 MB	View	Download
WebM *	450x360	345.34 kbits/sec	112.56 MB	View	Download
Flash Video	480x360	758.4 kbits/sec	247.65 MB	View	Download
iPod Video	480x360	505.35 kbits/sec	165.02 MB	View	Download
QuickTime	384x288	848.5 kbits/sec	277.07 MB	View	Download
MP3	44100 Hz	125.03 kbits/sec	40.61 MB	Listen	Download
Windows Media Video		475.47 kbits/sec	155.26 MB	View	Download
Auto	(Allows browser to choose a format it supports)