Transition to Chaos in Classical and Quantum Mechanics : Lectures Given at the 3rd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) Held in Montecatini Terme, Italy, July 6 - 13, 1991

How did Pierre Fatou and Gaston Julia create what we now call Complex Dynamics, in the context of the early twentieth century and especially of the First World War? The book is based partly on new, unpublished sources. Who were Pierre Fatou, Gaston Julia, Paul Montel? New biographical information is given on the little known mathematician that was Pierre Fatou. How did the WW1 injury of Julia influence mathematical life in France? From the reviews of the French version: "Audin’s book is ... filled with marvelous biographical information and analysis, dealing not just with the men mentioned in the book’s title but a large number of other players, too ... [It] addresses itself to scholars for whom the history of mathematics has a particular resonance and especially to mathematicians active, or even with merely an interest, in complex dynamics. ... presents it all to the reader in a very appealing form." (Michael Berg, The Mathematical Association of America, October 2009) Conté: Non commutative methods in semiclassical analysis / J. Bellisard ; Equidistribution of periodic orbits: an overview of classical vs quantum results / M. Degli Esposti, S. Graffi, S.Isola ; Action minimizing orbits in hamiltonian systems / G. Forni, J.N. Mather The Session Was Intended To Give A Broad Survey Of The Mathematical Problems Arising In The Chaotic Transition Of Deterministic Dynamical Systems, Both In Classical And Quantum Mechanics. The Lectures Of Mather And Forni Thoroughly Cover The Area- Preserving Twist Maps, And Include An Up-to-date Version Of The Aubry-mather Theory. The Lectures Of Bellissard Describe The Quantum Aspects: Classical Limit, Localization, Spectral Properties Of The Relevant Schrödinger Operators And Thus Represent An Exhaus- Tive Introduction To The Mathematics Of Quantum Chaos. The Lectures Of Degli Esposti Et Al. Reviews Equidistribu- Tion Of Unstable Periodic Orbits And Classical Limit Of Quantized Toral Symplectomorphisms. Non Commutative Methods In Semiclassical Analysis / J. Bellisard ---- Equidistribution Of Periodic Orbits: An Overview Of Classical Vs Quantum Results / M. Degli Esposti, S. Graffi, S. Isola ---- Action Minimizing Orbits In Hamiltonian Systems / G. Forni, J.n. Mather. J. Bellissard ... [et Al.] ; Editor, S. Graffi. Includes Bibliographical References.