Dynamics on Bi-Lagrangian Structures and Cherry maps

2025/08/17 by Ndawa, Bertuel Tangue
#53D05 #53D12 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.12350

Abstract

We consider a bi-Lagrangian structure (ω,F₁,F₂) on a manifold M, that is, (M,ω,F₁,F₂) is a bi-Lagrangian manifold. We prolong bi-Lagrangian structures on M, and lift a dynamic on its tangent and cotangent bundles in different ways. In some cases, we show that the lifted structures are affine. In the case of the 2-dimensional torus, we find that an extension of the same dynamic on pairs of so-called Cherry vector fields induces a conjugation action on a subset of Cherry maps (circle maps with a flat). Additionally, we define the linear connections for certain Cherry maps.

Citations

• Infinite Lifting of an Action of Symplectomorphism Group on the set of Bi-Lagrangian Structures

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