ISBN-13: 978-0126017106 ISBN-10: 0126017107

Elements of Differentiable Dynamics and Bifurcation Theory

Science & Math

Ruelle, David

Mathematics

Academic Pr

How do scientists look at chance, or randomness, and chaos in physical systems? In this study, David Ruelle explores game theory, probability, classical chaos and quantum uncertainty among many other topics. Since many systems are highly sensitive to initial conditions, the consequences of tiny exchanges in the variables can be enormous. Ruelle applies this insight to the understanding of turbulence, "strange attractors", entropy, black holes, information and intelligence.

Chance and Chaos

Penguin Putnam~trade

This classic book marks the beginning of an era of vigorous mathematical progress in equilibrium statistical mechanics. Its treatment of the infinite system limit has not been superseded, and the discussion of thermodynamic functions and states remains basic for more recent work. The conceptual foundation provided by the Rigorous Results remains invaluable for the study of the spectacular developments of statistical mechanics in the second half of the 20th century.

Statistical Mechanics: Rigorous Results (Advanced Book Classics)

Physics

Addison-Wesley

This book is aimed at mathematicians interested in such topics as ergodic theory, topological dynamics, constructive quantum field theory, the study of certain differentiable dynamical systems, notably Anosov diffeomorphisms and flows. It is also of interest to theoretical physicists concerned with the conceptual basis of equilibrium statistical mechanics. The level of the presentation is generally an advanced one, with the objective of providing an efficient research tool and a text for use in graduate teaching.

Thermodynamic Formalism: The Mathematical Structures of Classical Equilibrium Statistical Mechanics

Addison-Wesley Pub

Thermodynamic Formalism (Encyclopedia of Mathematics and its Applications, Series Number 5)

Reference

Encyclopedias & Subject Guides

Cambridge University Press

How do scientists look at chance, or randomness, and chaos in physical systems? In answering this question for a general audience, Ruelle writes in the best French tradition: he has produced an authoritative and elegant book-a model of clarity, succinctness, and a humor bordering at times on the sardonic.

Princeton University Press

How do scientists look at chance, or randomness, and chaos in physical systems? In answering this question for a general audience, Ruelle writes in the best French tradition: he has produced an authoritative and elegant book--a model of clarity, succinctness, and a humor bordering at times on the sardonic.

Chance and Chaos (Princeton Science Library)

The Mathematician's Brain poses a provocative question about the world's most brilliant yet eccentric mathematical minds: were they brilliant because of their eccentricities or in spite of them? In this thought-provoking and entertaining book, David Ruelle, the well-known mathematical physicist who helped create chaos theory, gives us a rare insider's account of the celebrated mathematicians he has known-their quirks, oddities, personal tragedies, bad behavior, descents into madness, tragic ends, and the sublime, inexpressible beauty of their most breathtaking mathematical discoveries.
 Consider the case of British mathematician Alan Turing. Credited with cracking the German Enigma code during World War II and conceiving of the modern computer, he was convicted of "gross indecency" for a homosexual affair and died in 1954 after eating a cyanide-laced apple--his death was ruled a suicide, though rumors of assassination still linger. Ruelle holds nothing back in his revealing and deeply personal reflections on Turing and other fellow mathematicians, including Alexander Grothendieck, René Thom, Bernhard Riemann, and Felix Klein. But this book is more than a mathematical tell-all. Each chapter examines an important mathematical idea and the visionary minds behind it. Ruelle meaningfully explores the philosophical issues raised by each, offering insights into the truly unique and creative ways mathematicians think and showing how the mathematical setting is most favorable for asking philosophical questions about meaning, beauty, and the nature of reality.
 The Mathematician's Brain takes you inside the world--and heads--of mathematicians. It's a journey you won't soon forget.

The Mathematician's Brain: A Personal Tour Through the Essentials of Mathematics and Some of the Great Minds Behind Them

This text marks the beginning of an era of vigorous mathematical progress in equilibrium statistical mechanics. It treats the infinite system limit, and discusses thermodynamic functions and states. The conceptual foundation provided by the book should be useful for the study of developments of statistical mechanics in the second half of the 20th century.

Statistical Mechanics: Rigorous Results (Icn-UCLA Symposia on Molecular & Cellular Biology)

W. A. Benjamin Advanced Bk Program

Consider a space $M$, a map $f:M\to M$, and a function $g:M \to {\mathbb C}$. The formal power series $\zeta (z) = \exp \sum ^\infty _{m=1} \frac {z^m}{m} \sum _{x \in \mathrm {Fix}\,f^m} \prod ^{m-1}_{k=0} g (f^kx)$ yields an example of a dynamical zeta function. Such functions have unexpected analytic properties and interesting relations to the theory of dynamical systems, statistical mechanics, and the spectral theory of certain operators (transfer operators). The first part of this monograph presents a general introduction to this subject. The second part is a detailed study of the zeta functions associated with piecewise monotone maps of the interval $[0,1]$. In particular, Ruelle gives a proof of a generalized form of the Baladi-Keller theorem relating the poles of $\zeta (z)$ and the eigenvalues of the transfer operator. He also proves a theorem expressing the largest eigenvalue of the transfer operator in terms of the ergodic properties of $(M,f,g)$.

Dynamical Zeta Functions for Piecewise Monotone Maps of the Interval (CRM Monograph Series)

Amer Mathematical Society

See the best price to sell, buy, or rent books by Ruelle, David. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Ruelle, David

See the best price to sell, buy, or rent books by Ruelle, David. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Elements of Differentiable Dynamics and Bifurcation Theory

Chance and Chaos

Statistical Mechanics: Rigorous Results (Advanced Book Classics)

Thermodynamic Formalism: The Mathematical Structures of Classical Equilibrium Statistical Mechanics

Thermodynamic Formalism (Encyclopedia of Mathematics and its Applications, Series Number 5)

Chance and Chaos

Chance and Chaos (Princeton Science Library)

The Mathematician's Brain: A Personal Tour Through the Essentials of Mathematics and Some of the Great Minds Behind Them

Statistical Mechanics: Rigorous Results (Icn-UCLA Symposia on Molecular & Cellular Biology)

Dynamical Zeta Functions for Piecewise Monotone Maps of the Interval (CRM Monograph Series)