Kategoria BISAC: Mathematics >> Differential Equations - General

Comment Fatou et Julia ont invente ce que l on appelle aujourd hui les ensembles de Julia, avant, pendant et apres la premiere guerre mondiale? L histoire est racontee, avec ses mathematiques, ses conflits, ses personnalites. Elle est traitee a partir de sources nouvelles, et avec rigueur. On pourra s y initier a l iteration des fractions rationnelles et a la dynamique complexe (ensembles de Julia, de Mandelbrot, ensembles-limites). Qui etaient Pierre Fatou, Gaston Julia, Paul Montel? On y trouvera en particulier des informations sur un mathematicien mal connu, Pierre Fatou. On decouvrira...

This book discusses the complex theory of differential equations or more precisely, the theory of differential equations on complex-analytic manifolds.

Although the theory of differential equations on real manifolds is well known it is described in thousands of papers and its usefulness requires no comments or explanations to date specialists on differential equations have not focused on the complex theory of partial differential equations. However, as well as being remarkably beautiful, this theory can be used to solve a number of problems in real theory, for instance, the Poincare...

Focusing on the theory of shadowing of approximate trajectories (pseudotrajectories) of dynamical systems, this book surveys recent progress in establishing relations between shadowing and such basic notions from the classical theory of structural stability as hyperbolicity and transversality.

Special attention is given to the study of "quantitative" shadowing properties, such as Lipschitz shadowing (it is shown that this property is equivalent to structural stability both for diffeomorphisms and smooth flows), and to the passage to robust shadowing (which is also equivalent to...

This book addresses the issue of uniqueness of a solution to a problem – a very important topic in science and technology, particularly in the field of partial differential equations, where uniqueness guarantees that certain partial differential equations are sufficient to model a given phenomenon. 

From the reviews: " ...] An excellent textbook in the theory of linear operators in Banach and Hilbert spaces. It is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory. ...] I can recommend it for any mathematician or physicist interested in this field." Zentralblatt MATH

This book presents models written as partial differential equations and originating from various questions in population biology, such as physiologically structured equations, adaptive dynamics, and bacterial movement. Its purpose is to derive appropriate mathematical tools and qualitative properties of the solutions. The book further contains many original PDE problems originating in biosciences.