Contents - ChaosBook

CONTENTSxI Convergence of spectral determinants 727I.1 Curvature expansions: geometric picture ..............727I.2 On importance of pruning ......................730I.3 Ma-the-matical caveats .......................731I.4 Estimate of the nth cumulant ....................732J Infinite dimensional operators 734J.1 Matrix-valued functions .......................734J.2 Operator norms ...........................736J.3 Trace class and Hilbert-Schmidt class ...............737J.4 Determinants of trace class operators ................739J.5 Von Koch matrices .........................742J.6 Regularization ............................744exercises 746 references 746K Statistical mechanics recycled 748K.1 The thermodynamic limit ......................748K.2 Ising models .............................750K.3 Fisher droplet model ........................753K.4 Scaling functions ..........................759K.5 Geometrization ...........................762résumé 769 commentary 769 exercises 769 references 770L Noise/quantum corrections 773L.1 Periodic orbits as integrable systems ................773L.2 The Birkhoff normal form .....................777L.3 Bohr-Sommerfeld quantization of periodic orbits .........778L.4 Quantum calculation of corrections ................780references 786S Solutions 789T Projects 864T.1 Deterministic diffusion, zig-zag map ................866references 870T.2 Deterministic diffusion, sawtooth map ...............872