Characterization of Attractors in Gumowski-Mira Map Using Fast Lyapunov Indicators

L. M. Saha¹*, M. K. Das² and Mridula Budhraja³

¹Department of Mathematics, Zakir Husain College, University of Delhi, Delhi-110002, India
²Institute of Informatics and Communication, University of Delhi South Campus, NewDelhi-110021, India
³Department of Mathematics, Shivaji College, University of Delhi, New Delhi-110027, India
*E-mail address: lmsaha@sify.com, mrinal@iic.ac.in, nkbudhraja@yahoo.com

(Received May 18, 2006; Accepted June 30, 2006)

Keywords: Fast Lyapunov Indicator, Gumowski-Mira Map

Abstract. In this Letter we have studied the behavior of the Fast-Lyapunov Indicators for various attractors of the Gumowski-Mira map. It was observed that the Fast-Lyapunov indicators show a typical type of behavior for different kinds of attractors, viz. chaotic, periodic, and bounded attractors. We have shown the possibility of a transient chaos in GM-map. The importance of FLI in dynamical system or maps is suggested.