過去の記録 ~06/17次回の予定今後の予定 06/18~

担当者 河野俊丈


17:00-17:50   数理科学研究科棟(駒場) 002号室
Hans-Otto Walther 氏 (University of Giessen)
Shilnikov chaos due to state-dependent delay, by means of the fixed point index
[ 講演概要 ]
What can variability of a delay in a delay differential equation do to the dynamics? We find a bounded delay functional d(¥phi), with d(¥phi)=1 on a neighborhood of ¥phi=0, such that the equation x'(t)=-a x(t-d(x_t)) has a solution which is homoclinic to 0, with shift dynamics in its vicinity, whereas the linear equation x'(t)=-a x(t-1) with constant time lag, for small solutions, is hyperbolic with 2-dimensional unstable space.
The proof involves regularity properties of the semiflow close to the homoclinic loop in the solution manifold and a generalization of a method due to Piotr Zgliczynsky which uses the fixed point index and a closing argument in order to establish shift dynamics when certain covering relations hold. (Joint work with Bernhard Lani-Wayda)
[ 参考URL ]