Author

Qiao Huang

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Preprint Aug 2026

Invariant connections in geometric mechanics: reduction, nonlocality, and curvature effects

We present a systematic study on the role of invariant connections in geometric mechanics. We first develop a comprehensive theory of reduction under left- and right-invariant connections on Lie groups, showing that the Euler--Poincar\'e and Lie--Poisson equations are independent of the connection. We then introduce a...

Huang Qiao · 0 citations

Preprint Jul 2026

Geometric Methods for Stochastic Dynamical Systems

Geometric methods are indispensable for analyzing, predicting, and mitigating the complex behaviors inherent in nonlinear systems. In this regime, the most probable transition path minimizes the Onsager-Machlup action functional, marking the likeliest route across an energy barrier. Lifting the analysis from individual...

Jin-Qiao Duan, Ting Gao, Qiao Huang et al. · 0 citations