Temporary list of contents of the book
"Aspects of the ergodic, qualitative and statistical theory of motion"
by Giovanni Gallavotti, Federico Bonetto, Guido Gentile



Sec (CHAPTER I: General qualitative properties)[1]
Sec (\${1.1} Historical note)[1]
Sec (\${1.2} Examples and some definitions)[4]
Sec (Appendix \${1.2}: Basic definitions of measure theory)[10]
Sec (\${1.3} Harmonic oscillators and integrable systems as dynamical systems)[13]
Sec (\${1.4} Frequencies of visit)[17]
Sec (Appendix \${1.4}: Analytically regular sets in $\hbox {\msytwww R}^n$ and $\hbox {\msytwww T}^n$)[23]
Sec (CHAPTER II: Ergodicity and ergodic points)[27]
Sec (\${2.1} Quasi-periodic motions and integrability)[27]
Sec (\${2.2} Ergodic properties of quasi-periodic motions. Ergodic sequences and measures.)[32]
Sec (Appendix \${2.2}: Birkhoff's theorem)[39]
Sec (\${2.3} Ergodic points)[50]
Sec (\${2.4} The ergodic decomposition)[60]
Sec (CHAPTER III: Entropy and complexity)[69]
Sec (\${3.1} Complexity of motions and entropy)[69]
Sec (\${3.2} The Shannon--McMillan theorem)[77]
Sec (\${3.3} Elementary properties of the average entropy)[87]
Sec (\${3.4} Further properties of the average entropy. Generator theorem)[93]
Sec (CHAPTER IV: Markovian pavements)[103]
Sec (\${4.1} Histories compatibility. Markovian pavements)[103]
Sec (\${4.2} Markovian pavements for hyperbolic systems)[112]
Sec (\${4.3} Coding of the volume measure of smooth hyperbolic systems)[133]
Sec (CHAPTER V: Gibbs distributions)[145]
Sec (\${5.1} Gibbs distributions)[145]
Sec (\${5.2} Properties of Gibbs distributions)[155]
Sec (\${5.3} Gibbs distributions on {$\hbox {\msytw Z}^+$})[160]
Sec (\${5.4} An application: expansive maps of $[0,1]$)[169]
Sec (CHAPTER VI: General properties of Gibbs' and SRB distributions.)[177]
Sec (\${6.1} Variational properties of Gibbs distributions)[177]
Sec (\${6.2} Applications to Anosov systems. SRB distribution.)[186]
Sec (\${6.3} Periodic orbits, invariant probability distributions and entropy)[196]
Sec (\${6.4} Equivalent potentials. Gibbs distributions with transitive vacuum)[203]
Sec (Appendix \${6.4}: Vanishing dispersion conditions)[209]
Sec (CHAPTER VII: Analyticity, singularity and phase transitions)[213]
Sec (\${7.1} Polymers)[213]
Sec (\${7.2} Cluster expansions.)[226]
Sec (Appendix \${7.2}: The classical expansion)[236]
Sec (\${7.3} Renormalization by decimation in one dimensional systems)[242]
Sec (\${7.4} Absence of phase transitions: more criteria)[255]
Sec (\${7.5} Phase transitions)[261]
Sec (CHAPTER VIII: Special ergodic theory problems in nonchaotic dynamics)[275]
Sec (\${8.1} Theory of quasi-periodic Hamiltonian motions)[275]
Sec (\${8.2} Graphs and diagrams for the Lindstedt series)[283]
Sec (\${8.3} Cancellations)[291]
Sec (Appendix \${8.3}: Extension of the Siegel-Bryuno bound.)[297]
Sec (\${8.4} Convergence and KAM theorem)[299]
Sec (Appendix \${8.4}: Weakening the strong Diophantine condition)[305]
Sec (CHAPTER IX: Some special topics in KAM theory)[309]
Sec (\${9.1} Resummations and renormalized series for invariant tori)[309]
Sec (\${9.2} Bounds on renormalized series. Convergence)[314]
Sec (Appendix \${9.2}: Resonances and low dimensional invariant tori)[320]
Sec (\${9.3} Scaling laws for the standard map)[322]
Sec (\${9.4} Scaling laws for the standard map)[332]
Sec (CHAPTER X: Special problems in chaotic dynamics)[339]
Sec (\${10.1} Perturbing Arnold's cat map)[339]
Sec (\${10.2} Extended systems. Lattices of Arnold's cat maps)[345]
Sec (\${10.3} Chaos in time: an SRB distribution)[351]
Sec (\${10.4} Chaos in space--time and SRB distributions)[360]
Sec (\${10.5} Isomorphisms)[371]
Sec (GLOBAL APPENDIX: Nonequilibrium thermodynamics ? twentyseven comments)[377]
Sec (Bibliography)[391]
Sec (Author index)[404]
Sec (Subject index)[405]
Sec (Citations index)[411]