Dynamics Beyond Uniform Hyperbolicity: A Global Geometric by Christian Bonatti,Lorenzo J. Díaz,Marcelo Viana

By Christian Bonatti,Lorenzo J. Díaz,Marcelo Viana

The proposal of uniform hyperbolicity, brought by way of Steve Smale within the early sixties, unified vital advancements and ended in a remarkably profitable conception for a wide type of platforms: uniformly hyperbolic platforms usually show advanced evolution which, however, is now very well understood, either geometrically and statistically. one other revolution has been occurring within the final couple of many years, as one attempts to construct a world thought for 'most' dynamical structures, getting better up to attainable of the conclusions of the uniformly hyperbolic case, in nice generality. This booklet goals to place such fresh advancements in a unified viewpoint, and to show open difficulties and sure instructions for extra development. it truly is geared toward researchers, either younger and senior, keen to get a brief, but wide, view of this a part of dynamics. major principles, equipment, and effects are mentioned, at variable levels of intensity, with references to the unique works for info and complementary information.

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