The connection whose holonomy is the classical adiabatic angles of Hannay and Berry and its generalization to the non-integrable case. (English) Zbl 0689.58043

We show how averaging defines an Ehresman connection whose holonomy is the classical adiabatic angles which Hannay defined for families of completely integrable systems. The averaging formula we obtain for the connection only requires that the family of Hamiltonians has a continuous symmetry group this allows us to extend the notion of Hannay angles to families of non-integrable systems with symmetry. We state three geometric axioms satisfied by the connection. These axioms uniquely determine the connection thus enabling us to find new formulas for the connection and its curvature. Two examples are given.
Reviewer: R.Schmid


58Z05 Applications of global analysis to the sciences
53C05 Connections (general theory)
70G99 General models, approaches, and methods in mechanics of particles and systems
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