Preface |
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ix | |
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The origins of Hamiltonian diffeomorphisms |
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1 | (2) |
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Flows and paths of diffeomorphisms |
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3 | (1) |
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4 | (2) |
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The group of Hamiltonian diffeomorphisms |
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6 | (4) |
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Algebraic properties of Ham (M, Ω) |
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10 | (3) |
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13 | (1) |
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Biinvariant geometries on Ham (M, Ω) |
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14 | (1) |
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The choice of the norm: Lp vs. L∞ |
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15 | (1) |
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The concept of displacement energy |
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16 | (5) |
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21 | (2) |
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23 | (3) |
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Estimating the displacement energy |
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26 | (3) |
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Introducing the ∂-operator |
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29 | (2) |
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The boundary value problem |
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31 | (1) |
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An application to the Liouville class |
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32 | (1) |
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33 | (4) |
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The space of periodic Hamiltonians |
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37 | (2) |
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39 | (2) |
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Paths in a given homotopy class |
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41 | (2) |
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Exact Lagrangian isotopies |
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43 | (3) |
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46 | (2) |
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An application to Hamiltonian loops |
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48 | (3) |
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51 | (1) |
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52 | (2) |
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54 | (1) |
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55 | (2) |
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Invariant tori of classical mechanics |
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57 | (2) |
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Growth of one-parameter subgroups |
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59 | (4) |
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Curve shortening in Hofer's geometry |
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63 | (1) |
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What happens when the asymptotic growth vanishes? |
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64 | (1) |
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The positive and negative parts of Hofer's norm |
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65 | (1) |
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Symplectic fibrations over S2 |
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66 | (3) |
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69 | (5) |
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An application to length spectrum |
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74 | (1) |
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Deformations of Symplectic Forms |
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75 | (1) |
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76 | (2) |
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An application to coupling |
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78 | (1) |
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Pseudo-holomorphic curves |
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79 | (2) |
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Persistence of exceptional spheres |
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81 | (2) |
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Hamiltonian loops as dynamical objects |
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83 | (2) |
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The asymptotic length spectrum |
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85 | (2) |
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87 | (2) |
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89 | (3) |
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92 | (1) |
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Stability and conjugate points |
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93 | (1) |
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The second variation formula |
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94 | (5) |
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Analysis of the second variation formula |
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99 | (2) |
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Length minimizing geodesics |
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101 | (4) |
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105 | (2) |
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Morse homology in finite dimensions |
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107 | (2) |
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109 | (4) |
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An application to geodesics |
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113 | (2) |
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115 | (2) |
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Non-Hamiltonian Diffeomorphisms |
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117 | (2) |
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119 | (2) |
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Links to ``hard'' symplectic topology |
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121 | (1) |
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Isometries in Hofer's geometry |
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122 | (3) |
Bibliography |
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125 | (6) |
Index |
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131 | (2) |
List of Symbols |
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133 | |