GEOMETRIC LORENZ ATTRACTOR AND ORBITAL SHADOWING PROPERTY
نویسندگان
چکیده
منابع مشابه
The fractal property of the Lorenz attractor
In a 1963 paper, Lorenz inferred that the Lorenz attractor must be an infinite complex of surfaces. We investigate this fractal property of the Lorenz attractor in two ways. Firstly, we obtain explicit plots of the fractal structure of the Lorenz attractor using symbolic dynamics and multiple precision computations of periodic orbits. The method we derive for multiple precision computation is b...
متن کاملOn Periodic Shadowing Property
In this paper, some properties of the periodic shadowing are presented. It is shown that a homeomorphism has the periodic shadowing property if and only if so does every lift of it to the universal covering space. Also, it is proved that continuous mappings on a compact metric space with the periodic shadowing and the average shadowing property also have the shadowing property and then are chao...
متن کاملThe Lorenz Attractor Exists
We prove that the Lorenz equations support a strange attractor, as conjectured by Ed-ward Lorenz in 1963. We also prove that the attractor is robust, i.e., it persists under small perturbations of the coeecients in the underlying diierential equations. The proof is based on a combination of normal form theory and rigorous numerical computations.
متن کاملNondensity of the Orbital Shadowing Property in C-topology
The orbital shadowing property (OSP) of discrete dynamical systems on smooth closed manifolds is considered. The nondensity of OSP with respect to the C1-topology is proved. The proof uses the method of skew products developed by Ilyashenko and Gorodetskĭı.
متن کاملThe Lorenz Attractor Is Mixing
We study a class of geometric Lorenz flows, introduced independently by Afrăımovič, Bykov & Sil′nikov and by Guckenheimer & Williams, and give a verifiable condition for such flows to be mixing. As a consequence, we show that the classical Lorenz attractor is mixing.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the Korean Mathematical Society
سال: 2016
ISSN: 1015-8634
DOI: 10.4134/bkms.2016.53.2.581