Books written by David Ruelle

Statistical Mechanics: Rigorous Results

The estimates ( 4.14 ) and ( 4.20 ) present a more serious problem ; we replace them by the use of the following results . 3.5.9 PROPOSITION . If A + 0 ( Fisher ) , V ( A ) -in + p and V ( A ) - ' E → 00 , then the points ( V ( A ) ...
Turbulence, Strange Attractors, and Chaos

Then for u near 0 , by a u dependent coordinate change in R ?, one can bring in the following form : Pu ( r ... An example of “ decay ” ( loss of differentiability ) of T2 under perturbations has been studied by N. Levinson [ a second ...
The Mathematician's Brain: A Personal Tour Through the Essentials of Mathematics and Some of the Great Minds Behind Them

Eventually he went to the United States, where he pursued a brilliant mathematical career, which eventually led to the Weil conjectures. The later proof of these conjectures by Grothendiek6 and Pierre Deligne7 was an important moment in ...
Elements of Differentiable Dynamics and Bifurcation Theory

Theorem (Pugh)." Let g be the subset of Diff'(M) or A*(M) consisting of diffeomorphisms or flows such that the periodic orbits are dense in the nonwandering set Q (i.e., the closure of the union of the periodic orbits is Q).
Mecanique Statistique Et Theorie Quantique Des Champs

Mecanique Statistique Et Theorie Quantique Des Champs
La mente matematica

Si ammette che i moltiplicato per se stesso (cioè i2) sia uguale a –1. ... 1 x + iy iy Ora tracciamo due rette nel piano che si incontrano perpendicolarmente in O. Chiamiamole asse x (Ox) e asse y (Oy), come nella figura qui sotto. x x2 ...
Chance and Chaos

How do scientists look at chance, or randomness, and chaos in physical systems?
Chance and Chaos

... probability 0 ( zero percent ) corresponds to impossibility and the probability 1 ( one hundred percent ) to certainty . If the probability of an event is neither 0 nor 1 , then this event is uncertain , but our uncertainty about it is ...
The Mathematician's Brain

This book provides an account of celebrated mathematicians and their quirks, oddities, personal tragedies, bad behavior, descents into madness, tragic ends, and the beauty of their mathematical discoveries.