NONDENSE ORBITS FOR ANOSOV DIFFEOMORPHISMS OF THE 2-TORUS

Jimmy Tseng

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NONDENSE ORBITS FOR ANOSOV DIFFEOMORPHISMS OF THE 2-TORUS

机译：2-托洛斯的阿诺索夫微形态的非密集轨道

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摘要

Let λ denote the probability Lebesgue measure on T_2. For any C~2-Anosov diffeomorphism of the 2-torus preserving λ with measure-theoretic entropy equal to topological entropy, we show that the set of points with nondense orbits is hyperplane absolute winning (HAW). This generalizes the result in [18, Theorem 1.4] for C_2-expanding maps of the circle.

机译：令λ表示对T_2的概率Lebesgue测度。对于度量理论熵等于拓扑熵的保有2个环的λ的任何C〜2-Anosov微分，我们证明具有非密集轨道的点集是超平面绝对获胜（HAW）。这将在[18，定理1.4]中针对圆的C_2展开图推广了结果。

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来源
《Real analysis exchange》 |2016年第2期|307-314|共8页
作者
Jimmy Tseng;
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作者单位

School of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW, UK;

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原文格式 PDF
正文语种 eng
中图分类
关键词
nondense orbits; Anosov diffeomorphisms; winning sets;

机译：非密集轨道阿诺索夫亚型;胜利套;

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专利

1. A special ergodic theorem for Anosov diffeomorphisms on the 2-torus [J] . Saltykov P.S. Functional analysis and its applications . 2011,第1期

机译：2-torus上Anosov微分同构的特殊遍历定理
2. Diffeomorphisms approximated by anosov on the 2-Torus and their SBR measures [J] . Naoya Sumi Transactions of the American Mathematical Society . 1999,第8期

机译：由Anosov在2-Torus上近似的微分同构及其SBR测度
3. Quasi-Anosov diffeomorphisms and pseudo-orbit tracing property [J] . Kazuhiro Sakai Nagoya Mathematical Journal . 1988,第4期

机译：拟Anosov微分态和伪轨道跟踪性质
4. ANOSOV DIFFEOMORPHISMS [C] . Joao P. Almeida, Albert M. Fisher, Alberto A. Pinto AIMS International Conference on Dynamical Systems, Differential Equations and Applications . 2013

机译：Anosov Diffeomorphisms.
5. Pseudo-Anosov diffeomorphisms in the unit disk and a new proof of the uniqueness of a Teichmuller line left invariant by a hyperbolic modular transformation. [D] . Slutskin, Lev. 1987

机译：单位圆盘中的伪-Anosov微分和通过双曲模数变换不变地保持不变的Teichmuller线的唯一性的新证明。
6. Nondense mammographic area and risk of breast cancer [O] . Andreas Pettersson, Susan E Hankinson, Walter C Willett, 2011

机译：非密集乳腺X线摄影区域和患乳腺癌的风险
7. Nondense orbits for Anosov diffeomorphisms of the 2-torus [O] . Tseng Jimmy 2016

机译：2-torus Anosov微分同构的非密集轨道
8. Stably Bernoullian Diffeomorphism That Is Not Anosov [R] . Shub, M., Wilkinson, A. 1998

机译：稳定的伯努利非均匀性不是阿诺索夫

NONDENSE ORBITS FOR ANOSOV DIFFEOMORPHISMS OF THE 2-TORUS

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