不连续流的拓扑压

兰州理工大学学报 ›› 2025, Vol. 51 ›› Issue (4): 147-151.

不连续流的拓扑压

张俊杰¹, 梁雅丽^2,3, 王威^*4

1.苏州科技大学数学科学学院, 江苏苏州 215009;
2.上海旅游高等专科学校酒店与烹饪学院, 上海 201418;
3.上海师范大学旅游学院, 上海 200234;
4.南通理工学院基础教学学院, 江苏南通 226002

收稿日期:2023-07-07 出版日期:2025-08-28 发布日期:2025-09-05
通讯作者: 王威(1978-),男,安徽寿县人,副教授.Email:39658255@qq.com
基金资助:
江苏省研究生科研创新计划(KYCX23_3300),上海市“晨光计划”(20CGB09)

Topological pressure for discontinuous flows

ZHANG Jun-jie¹, LIANG Ya-li^2,3, WANG Wei⁴

1. School of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou 215009, China;
2. School of Hospitality and Culinary Arts, Shanghai Institute of Tourism, Shanghai 201418, China;
3. School of Tourism, Shanghai Normal University, Shanghai 200234, China;
4. School of General Education, Nantong Institute of Technology, Nantong 226002, China

Received:2023-07-07 Online:2025-08-28 Published:2025-09-05

摘要/Abstract

摘要： 给出在不连续半流上拓扑压的定义并研究其在不连续半流上的性质,证明了在连续半流的情况下,这些不连续流的拓扑压定义等价于经典拓扑压的定义.此外,给出了拓扑τ-压定义,并研究其与不连续流上的拓扑压的关系.

关键词: 不连续流, 动力系统, 拓扑τ-压

Abstract: Giving the definition of topological pressure on discontinuous semiflow andstudying its properties on discontinuous semiflow, these definitionsequalling to classical definition are proved in the case of continuous semiflow. In addition, topological τ-pressure is defined and its relationship with topological pressure on discontinuous semiflow is studied.

Key words: discontinuous semiflow, dynamical system, topological τ-pressure

中图分类号:

O192

张俊杰, 梁雅丽, 王威. 不连续流的拓扑压[J]. 兰州理工大学学报, 2025, 51(4): 147-151.

ZHANG Jun-jie, LIANG Ya-li, WANG Wei. Topological pressure for discontinuous flows[J]. Journal of Lanzhou University of Technology, 2025, 51(4): 147-151.

参考文献

[1] KOLMOGOROV A.A new metric invariant of transient dynamical systems and automorphisms in Lebesgue spaces[J].Doklady Akademii Nauk SSSR,1958,951(5):861-864.
[2] SINAI Y.Flows with finite entropy[J].Doklady Akademii Nauk SSSR,1959,125:1200-1202.
[3] ADLER R L,KONHEIM A G,MCANDREW M H.Topological entropy[J].Transactions of the American Mathematical Society,1965,114(2):309-319.
[4] DINABURG E I.A correlation between topological entropy and metric entropy[J].Doklady Akademii Nauk SSSR,1970,190:19-22.
[5] GOODWYN L W.Comparing topological entropy with measure-theoretic entropy[J].American Journal of Mathematics,1972,94(2):366-388.
[6] MISIUREWICZ M.A short proof of the variational principle for a Z^N₊ action on a compact space[J].Asterique,1976,40:147-187.
[7] BOWEN R.Entropy for group endomorphisms and homogeneous spaces[J].Transactions of the American Mathematical Society,1971,153:401-414.
[8] THOMAS R F.Entropy of expansive flows[J].Ergodic Theory and Dynamical Systems,1987,7(4):611-625.
[9] THOMAS R F.Topological entropy of fixed-point free flows[J].Transactions of the American Mathematical Society,1990,319(2):601-618.
[10] DOU D,FAN M,QIU H.Topological entropy on subsets for fixed-point free flows[J].Discrete and Continuous Dynamical Systems,2017,37(12):6319-6331.
[11] JAQUE N,MARTÍN B S.Topological entropy for discontinuous semiflows[J].Journal of Differential Equations,2019,266(6):3580-3600.
[12] JI Y,CHEN E,WANG Y,et al.Bowen entropy for fixed-point free flows[J].Discrete & Continuous Dynamical Systems:Series A,2019,39(11):6231-6239.
[13] WANG Y,CHEN E,LIN Z,et al.Bowen entropy of sets of generic points for fixed-point free flows[J].Journal of Differential Equations,2020,269(11):9846-9867.
[14] KELLER G.Equilibrium states in ergodic theory[M].Cambridge:MA,Cambridge University Press,1998.
[15] PESIN Y B.Dimension theory in dynamical systems:contemporary views and applications[M].Chicago:University of Chicago Press,1997.
[16] BOWEN R.Hausdorff dimension of quasi-circles[J].Publications Mathématiques de l’IHÉS,1979,50:11-25.
[17] RUELLE D.Repellers for real analytic maps[J].Ergodic Theory and Dynamical Systems,1982,2(1):99-107.
[18] BACKES L,RODRIGUES F B.Topological pressure for discontinuous semiflows and a variational principle for impulsive dynamical systems[J].Topological Methods in Nonlinear Analysis,2022,59(1):303-330.
[19] ALVES J F,CARVALHO M,VÁSQUEZ C H.A variational principle for impulsive semiflows[J].Journal of Differential Equations,2015,259(8):4229-4252.