【摘要】：齊性動(dòng)力系統(tǒng)是由李群給出的一類特殊動(dòng)力系統(tǒng),與Diophantine逼近等數(shù)論方向有著緊密的聯(lián)系.本文概述關(guān)于齊性動(dòng)力系統(tǒng)有界軌道的主要問(wèn)題和結(jié)果,并介紹它們與Oppenheim猜想、Littlewood猜想和Schmidt猜想等Diophantine逼近問(wèn)題的關(guān)系.
[Abstract]:Homogeneous dynamical system is a kind of special dynamical system given by Li Qun, which is closely related to the direction of number theory such as Diophantine approximation. In this paper, the main problems and results of bounded orbits for homogeneous dynamical systems are summarized, and their relations with Oppenheim's conjecture, Littlewood's conjecture and Schmidt's conjecture for Diophantine approximation are introduced.
【作者單位】： 北京大學(xué)數(shù)學(xué)科學(xué)學(xué)院;北京大學(xué)北京國(guó)際數(shù)學(xué)研究中心;
【基金】：國(guó)家自然科學(xué)基金(批準(zhǔn)號(hào):11322101)資助項(xiàng)目
【分類號(hào)】：O19
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本文編號(hào)：2470403