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arXiv · 2501.07568

Construction of approximate invariants for non-integrable Hamiltonian systems

Yongjun Li·Derong Xu·Yue Hao
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Abstract

We present a method to construct high-order polynomial approximate invariants (AI) for non-integrable Hamiltonian dynamical systems, and apply it to modern ring-based particle accelerators. Taking advantage of a special property of one-turn transformation maps in the form of a square matrix, AIs can be constructed order-by-order iteratively. Evaluating AI with simulation data, we observe that AI's fluctuation is actually a measure of chaos. Through minimizing the fluctuations with control knobs in accelerators, the stable region of long-term motions could be enlarged.

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Yongjun Li, Derong Xu, Yue Hao. 2025-01-13. Construction of approximate invariants for non-integrable Hamiltonian systems. https://doi.org/10.1103/m349-wmnr

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