Geometry of Diophanite exponents
نویسندگان
چکیده
Диофантовы экспоненты являются одними из самых простых количественных характеристик, отвечающих за аппроксимационные свойства линейных подпространств евклидова пространства. Данный обзор посвящeн описанию современного состояния раздела теории диофантовых приближений, изучающего диофантовы и соотношения, которым они удовлетворяют. Мы обсуждаем классические экспоненты, возникающие в задаче приближения нуля набором значений нескольких форм целых точках, их аналоги приближений с весами, мультипликативные а также решeток. Особое внимание уделяется принципу переноса. Библиография: 99 названий.
منابع مشابه
Lyapunov exponents in Hilbert geometry
We study the behaviour of a Hilbert geometry when going to infinity along a geodesic line. We prove that all the information is contained in the shape of the boundary at the endpoint of this geodesic line and have to introduce a regularity property of convex functions to make this link precise. The point of view is a dynamical one and the main interest of this article is in Lyapunov exponents o...
متن کاملPercolation fractal exponents without fractal geometry
Classically, percolation critical exponents are linked to the power laws that characterize percolation cluster fractal properties. It is found here that the gradient percolation power laws are conserved even for extreme gradient values for which the frontier of the infinite cluster is no more fractal. In particular the exponent 7/4 which was recently demonstrated to be the exact value for the d...
متن کاملI-Projection and the Geometry of Error Exponents
We present a geometric approach, using Iprojections [4], for analyzing error exponents in various information theory problems—e.g., hypothesis-testing, source coding, and channel coding. By illuminating on the hidden geometrical structure, it also clarifies the distribution of the log likelihood for correct and incorrect codewords. Calculating the error exponent for very noisy channels becomes ...
متن کاملGeometry of dynamics, Lyapunov exponents and phase transitions
The Hamiltonian dynamics of classical planar Heisenberg model is numerically investigated in two and three dimensions. By considering the dynamics as a geodesic flow on a suitable Riemannian manifold, it is possible to analytically estimate the largest Lyapunov exponent in terms of some curvature fluctuations. The agreement between numerical and analytical values for Lyapunov exponents is very ...
متن کاملconstruction of vector fields with positive lyapunov exponents
in this thesis our aim is to construct vector field in r3 for which the corresponding one-dimensional maps have certain discontinuities. two kinds of vector fields are considered, the first the lorenz vector field, and the second originally introced here. the latter have chaotic behavior and motivate a class of one-parameter families of maps which have positive lyapunov exponents for an open in...
15 صفحه اولذخیره 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: Uspehi matemati?eskih nauk
سال: 2023
ISSN: ['2305-2872', '0042-1316']
DOI: https://doi.org/10.4213/rm10089