2018/05/09 by Zhaodong Ding, Ding, Zhaodong, Zaijiu Shang +3
Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Dynamical Systems (math.DS) #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1805.03355
openalex publication_date 2018/05/09 · openalex created_date 2018/05/17 · openalex updated_date 2026/07/28
We prove a Nekhoroshev-type theorem for nearly integrable symplectic map. As an application of the theorem, we obtain the exponential stability symplectic algorithms. Meanwhile, we can get the bounds for the perturbation, the variation of the action variables, and the exponential time respectively. These results provide a new insight into the nonlinear stability analysis of symplectic algorithms. Combined with our previous results on the numerical KAM theorem for symplectic algorithms (2018), we give a more complete characterization on the complex nonlinear dynamical behavior of symplectic algorithms.