Noise, Oscillators and Algebraic Randomness [electronic resource] : From Noise in Communication Systems of Number Theory Lectures of a School Held in Chapelle des Bois, France, April 5–10, 1999 / edited by Michel Planat.

Mathemagics -- Thermal and Quantum Noise in Active Systems -- Dipole at ? = 1 -- Stored Ion Manipulation Dynamics of Ion Cloud and Quantum Jumps with Single Ions -- 1/f Fluctuations in Cosmic Ray Extensive Air Showers -- Stochastic Resonance and the Benefit of Noise in Nonlinear Systems -- Time is Money -- Oscillators and the Characterization of Frequency Stability: an Introduction -- Phase Noise Metrology -- Phonon Fine Structure in the 1/f Noise of Metals, Semiconductors and Semiconductor Devices -- The General Nature of Fundamental 1/f Noise in Oscillators and in the High Technology Domain -- 1/f Frequency Noise in a Communication Receiver and the Riemann Hypothesis -- Detection of Chaos in the Noise of Electronic Oscillators by Time Series Analysis Methods -- Geometry and Dynamics of Numbers Under Finite Resolution -- Diophantine Conditions and Real or Complex Brjuno Functions -- Algebraic and Analytic Randomness -- From Symbolic Dynamics to a Digital Approach: Chaos and Transcendence -- Algebraic Dynamics and Transcendental Numbers -- Dynamics of Some Contracting Linear Functions Modulo 1 -- On the Modular Function and Its Importance for Arithmetic -- On Generalized Markoff Equations and Their Interpretation.

Noise is ubiquitous in nature and in man-made systems. Noise in oscillators perturbs high-technology devices such as time standards or digital communication systems. The understanding of its algebraic structure is thus of vital importance. The book addresses both the measurement methods and the understanding of quantum, 1/f and phase noise in systems such as electronic amplifiers, oscillators and receivers, trapped ions, cosmic ray showers and in commercial applications. A strong link between 1/f noise and number theory is emphasized. The twenty papers in the book are comprehensive versions of talks presented at a School in Chapelle des Bois (Jura, France) held from April 6 to 10, 1999 by engineers, physisicts and mathematicians.