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

Introduction Michel Planat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Mathemagics (A Tribute to L. Euler and R. Feynman) Pierre Cartier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Part I Classical and Quantum Noise Thermal and Quantum Noise in Active Systems Jean-Michel Courty, Francesca Grassia, Serge Reynaud . . . . . . . . . . . . . . 71 Dipole at ƒث = 1 V. Pasquier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Stored Ion Manipulation Dynamics of Ion Cloud and Quantum Jumps with Single Ions Fernande Vedel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 1/f Fluctuations in Cosmic Ray Extensive Air Showers E. Faleiro, J.M.G. GپLomez . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Stochastic Resonance and the Benefit of Noise in Nonlinear Systems FranپCcois Chapeau-Blondeau . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Time is Money Marcel Ausloos, Nicolas Vandewalle, Kristinka Ivanova . . . . . . . . . . . . . . 156 Part II Noise in Oscillators, 1/f Noise and Arithmetic Oscillators and the Characterization of Frequency Stability: an Introduction Vincent Giordano, Enrico Rubiola. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 Phase Noise Metrology Enrico Rubiola, Vincent Giordano. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 VIII Contents Phonon Fine Structure in the 1/f Noise of Metals, Semiconductors and Semiconductor Devices Mihai N. Mihaila . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 The General Nature of Fundamental 1/f Noise in Oscillators and in the High Technology Domain Peter H. Handel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 1/f Frequency Noise in a Communication Receiver and the Riemann Hypothesis Michel Planat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 Detection of Chaos in the Noise of Electronic Oscillators by Time Series Analysis Methods C. Eckert, M. Planat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 Geometry and Dynamics of Numbers Under Finite Resolution Jacky Cresson, Jean-Nicolas DپLenariپLe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 Diophantine Conditions and Real or Complex Brjuno Functions Pierre Moussa, Stefano Marmi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 Part III Algebraic Randomness Algebraic and Analytic Randomness Jean-Paul Allouche . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 From Symbolic Dynamics to a Digital Approach K. Karamanos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 Algebraic Dynamics and Transcendental Numbers Michel Waldschmidt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 Dynamics of Some Contracting Linear Functions Modulo 1 Yann Bugeaud, Jean-Pierre Conze . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 On the Modular Function and Its Importance for Arithmetic Paula B. Cohen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388 On Generalized Markoff Equations and Their Interpretation Serge Perrine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398