An implicit algorithm for validated enclosures of the solutions to variational equations for ODEs

作者：

Highlights：

• An algorithm for validated computation of monodromy matrices for ODEs is provided.

• Smaller truncation error allows larger time steps making the computation faster.

• The existence of a chaotic and hyperbolic set for the Rossler system is proved via computer-assisted proofs techniques.

摘要

•An algorithm for validated computation of monodromy matrices for ODEs is provided.•Smaller truncation error allows larger time steps making the computation faster.•The existence of a chaotic and hyperbolic set for the Rossler system is proved via computer-assisted proofs techniques.

论文关键词：Validated numerics,Initial value problem,Variational equations,Uniform hyperbolicity,Chaos

论文评审过程：Received 1 October 2015, Revised 21 June 2016, Accepted 6 July 2016, Available online 25 July 2016, Version of Record 25 July 2016.

论文官网地址：https://doi.org/10.1016/j.amc.2016.07.005