A Topological Approach to the Algorithmic Computation of the Conley Index for Poincare Maps

作者：Mrozek Marian^*; Srzednicki Roman; Weilandt Frank

来源：SIAM Journal on Applied Dynamical Systems, 2015, 14(3): 1348-1386.

DOI：10.1137/15M100794X

• Poincare map
• Conley index
• interval arithmetic
• rigorous numerical algorithm

A new algorithm for computing the Conley index of the Poincare map of a time-periodic nonautonomous ordinary differential equation is presented. The algorithm is based on a theorem which reduces the computation of the index to the study of certain singular chains on an index pair for some small-step translation operator of the equation. In particular, no numerical enclosures of the Poincare map are required. Concrete numerical examples for planar systems are provided.

• 出版日期2015