Contents
Introduction, 1
§ 1 Some Examples, 3
§ 2 Reconstruction of dynamics for Hamiltonian systems, 19
§ 3 Reconstruction of dynamics for Lagrangian systems, 26
§ 4 Ehresmann connections and holonomy, 36
§ 5 Reconstruction phases, 42
§ 6 Averaging connections, 56
§ 7 Existence, uniqueness and curvature of the Hannay-Berry connections, 63
§ 8 The Hannay-Berry connection in the presence of additional symmetry, 69
§ 9 The Hannay-Berry connection on level sets of the momentum map, 74
§ 1 0 Case I: Bundles of symplectic manifolds with the canonical connection;
integrable systems, 76
§ 1 1 Case II: Cartan connections; moving systems, 87
§ 1 2 The Cartan angles; the ball in the hoop and the Foucault pendulum, 92
§
1 3 Induced connections on the tower of bundles, 98
§ 1 4 The Hannay-Berry connection for general systems, 104
References, 107
in
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