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arXiv · 2509.05998

q-Cosymplectic Geometry, Integrability and Reduction

Melvin Leok·Cristina Sardón·Xuefeng Zhao
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Abstract

In the present paper, we define the concept of a \( q \)-cosymplectic manifold, on which we study the Hamiltonian, gradient, local gradient, and \( q \)-evolution vector fields. Several Liouville--Arnold-type theorems and a \( q \)-cosymplectic Marsden--Weinstein reduction theorem are established. We also provide physical examples illustrating the application of the structure to multitime dynamics (Fast-slow dynamical system). To make our work more self-contained, we include detailed proofs for some results that may resemble those known for cosymplectic manifolds.

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Melvin Leok, Cristina Sardón, Xuefeng Zhao. 2025-09-07. q-Cosymplectic Geometry, Integrability and Reduction. https://arxiv.org/abs/2509.05998

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