On the construction of Lyapunov functions with computer assistance
作者：
Highlights：
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• A systematic procedure of Lyapunov functions around fixed points of dynamical systems with computer assistance.
• Validation of Lyapunov functions and their domains as “mathematically rigorous” objects.
• A topological property of Lyapunov domains providing a re-parameterization of trajectories, which ensures to validate blow-up solutions (e.g., Takayasu et al. (2017)).
• Numerical validation results exhibit the applicability of our method both for continuous and discrete dynamical systems.
摘要
•A systematic procedure of Lyapunov functions around fixed points of dynamical systems with computer assistance.•Validation of Lyapunov functions and their domains as “mathematically rigorous” objects.•A topological property of Lyapunov domains providing a re-parameterization of trajectories, which ensures to validate blow-up solutions (e.g., Takayasu et al. (2017)).•Numerical validation results exhibit the applicability of our method both for continuous and discrete dynamical systems.
论文关键词：34D05,37B25,65H10,Lyapunov functions,Computer-assisted proof and construction
论文评审过程：Received 12 July 2016, Revised 4 December 2016, Available online 27 January 2017, Version of Record 8 February 2017.
论文官网地址：https://doi.org/10.1016/j.cam.2017.01.002
