Discretization of Homoclinic Orbits, Rapid Forcing, and "Invisible Chaos"

by Jürgen Scheurle, Bernold Fiedler, Jurgen Scheurle

One-step discretizations of order $p$ and step size $e$ of autonomous ordinary differential equations can be viewed as time-$e$ maps of a certain first order ordinary differential equation that is a rapidly forced nonautonomous system. Fiedler and Scheurle study the behavior of a homoclinic orbit for $e = 0$, under discretization. Under generic assumptions they show that this orbit becomes transverse for positive $e$. Likewise, the region where complicated,...

• Format: Paperback
• Language: English
• ISBN: 0821804685
• ISBN13: 9780821804681
• Release Date: January 1996
• Publisher: American Mathematical Society(RI)
• Length: 79 Pages