Coexistence and Persistence of Strange Attractors (Lecture Notes in Mathematics)

Description:

Although chaotic behaviour had often been observed numerically earlier, the first mathematical proof of the existence, with positive probability (persistence) of strange attractors was given by Benedicks and Carleson for the Henon family, at the beginning of 1990's. Later, Mora and Viana demonstrated that a strange attractor is also persistent in generic one-parameter families of diffeomorphims on a surface which unfolds homoclinic tangency. This book is about the persistence of any number of strange attractors in saddle-focus connections. The coexistence and persistence of any number of strange attractors in a simple three-dimensional scenario are proved, as well as the fact that infinitely many of them exist simultaneously.

subjects: Chaotic behavior in systems,  Chaos theory,  Mathematics,  Chaos Theory (Mathematics),  Science,  Science/Mathematics,  System Theory,  Differential Equations,  History,  Mathematical Analysis,  Mathematics / Mathematical Analysis,  Mathematics-Differential Equations,  Science-History,  Differentiable dynamical systems,  Global analysis,  Global Analysis and Analysis on Manifolds,  Dynamical Systems and Ergodic Theory