کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4613609 1338767 2006 26 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A Grobman–Hartman theorem for nonuniformly hyperbolic dynamics
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
A Grobman–Hartman theorem for nonuniformly hyperbolic dynamics
چکیده انگلیسی

We establish a version of the Grobman–Hartman theorem in Banach spaces for nonuniformly hyperbolic dynamics. We also consider the case of sequences of maps, which corresponds to a nonautonomous dynamics with discrete time. More precisely, we consider sequences of Lipschitz maps Am+fm such that the linear parts Am admit a nonuniform exponential dichotomy, and we establish the existence of a unique sequence of topological conjugacies between the maps Am+fm and Am. Furthermore, we show that the conjugacies are Hölder continuous, with Hölder exponent determined by the ratios of Lyapunov exponents with the same sign. To the best of our knowledge this statement appeared nowhere before in the published literature, even in the particular case of uniform exponential dichotomies, although some experts claim that it is well known in this case. We are also interested in the dependence of the conjugacies on the perturbations fm: we show that it is Hölder continuous, with the same Hölder exponent as the one for the conjugacies. We emphasize that the additional work required to consider the case of nonuniform exponential dichotomies is substantial. In particular, we need to consider several additional Lyapunov norms.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 228, Issue 1, 1 September 2006, Pages 285-310