Noise, oscillators, and algebraic randomness : from noise in communication systems to number theory : lectures of a school held in Chapelle des Bois, France, April 5-10, 1999 / Michel Planat

Contents: Michel Planat, Introduction (1–5); Pierre Cartier, Mathemagics (a tribute to L. Euler and R. Feynman) (6–67); Jean-Michel Courty, Francesca Grassia and Serge Reynaud, Thermal and quantum noise in active systems (71–83); V. Pasquier, Dipole at ν=1 (84–106); Fernande Vedel, Stored ion manipulation dynamics of ion cloud and quantum jumps with single ions (107–124); E. Faleiro and J. M. G. Gómez, 1/f fluctuations in cosmic ray extensive air showers (125–136); François Chapeau-Blondeau, Stochastic resonance and the benefit of noise in nonlinear systems (137–155); Marcel Ausloos, Nicolas Vandewalle and Kristinka Ivanova, Time is money (156–171); Vincent Giordano and Enrico Rubiola, Oscillators and the characterization of frequency stability: an introduction (175–188); Enrico Rubiola and Vincent Giordano, Phase noise metrology (189–215); Mihai N. Mihaila, Phonon fine structure in the 1/f noise of metals, semiconductors and semiconductor devices (216–231); Peter H. Handel, The general nature of fundamental 1/f noise in oscillators and in the high technology domain (232–264); Michel Planat, 1/f frequency noise in a communication receiver and the Riemann hypothesis (265–287); C. Eckert and M. Planat, Detection of chaos in the noise of electronic oscillators by time series analysis methods (288–304); Jacky Cresson and Jean-Nicolas Dénarié, Geometry and dynamics of numbers under finite resolution (305–323); Pierre Moussa and Stefano Marmi, Diophantine conditions and real or complex Brjuno functions (324–342); Jean-Paul Allouche, Algebraic and analytic randomness (345–356); K. Karamanos, From symbolic dynamics to a digital approach: chaos and transcendence (357–371); Michel Waldschmidt, Algebraic dynamics and transcendental numbers (372–378); Yann Bugeaud and Jean-Pierre Conze, Dynamics of some contracting linear functions modulo 1 (379–387); Paula B. Cohen, On the modular function and its importance for arithmetic (388–397); Serge Perrine, On generalized Markoff equations and their interpretation (398–417).