26 citations · 28 across the 8 of their papers we have counts for
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math.DS2018
Numerical invariant tori of symplectic integrators for integrable Hamiltonian systems
Zhaodong Ding, Zaijiu Shang
In this paper, we study the persistence of invariant tori of integrable Hamiltonian systems satisfying Rüssmann's non-degeneracy condition when symplectic integrators are applied t…
math.DS2018★ 1 cited
Exponential Stability Estimate of Symplectic Integrators for Integrable Hamiltonian Systems
Zhaodong Ding, Zaijiu Shang, Bo Xie
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…
math.DS2018
A KAM-Theorem for Persistence of Quasi-periodic Invariant Tori in Bifurcation Theory of Equilibrium Points
Xuemei Li, Zaijiu Shang
In this paper, we establish a KAM-theorem for ordinary differential equations with finitely differentiable vector fields and multiple degeneracies. The theorem can be used to deal…