Browse > Article
http://dx.doi.org/10.4134/JKMS.j210258

KATOK-HASSELBLATT-KINEMATIC EXPANSIVE FLOWS  

Huynh, Hien Minh (Department of Mathematics and Statistics Quy Nhon University)
Publication Information
Journal of the Korean Mathematical Society / v.59, no.1, 2022 , pp. 151-170 More about this Journal
Abstract
In this paper we introduce a new notion of expansive flows, which is the combination of expansivity in the sense of Katok and Hasselblatt and kinematic expansivity, named KH-kinematic expansivity. We present new properties of several variations of expansivity. A new hierarchy of expansive flows is given.
Keywords
KH-kinematic expansivity; expansive flows; fixed points; dynamical systems;
Citations & Related Records
연도 인용수 순위
  • Reference
1 M. Komuro, Expansive properties of Lorenz attractors, in The theory of dynamical systems and its applications to nonlinear problems (Kyoto, 1984), 4-26, World Sci. Publishing, Singapore, 1984.
2 H. M. Huynh, Expansiveness for the geodesic and horocycle flows on compact Riemann surfaces of constant negative curvature, J. Math. Anal. Appl. 480 (2019), no. 2, 123425. https://doi.org/10.1016/j.jmaa.2019.123425   DOI
3 H. M. Huynh, A solution to Flinn's conjecture on weakly expansive flows, Ergodic Theory Dynam. Systems 41 (2021), no. 5, 1390-1396. https://doi.org/10.1017/etds.2020.9   DOI
4 H. B. Keynes and M. Sears, F-expansive transformation groups, General Topology Appl. 10 (1979), no. 1, 67-85.   DOI
5 A. Artigue, Expansive flows of surfaces, Discrete Contin. Dyn. Syst. 33 (2013), no. 2, 505-525. https://doi.org/10.3934/dcds.2013.33.505   DOI
6 T. Fisher and B. Hasselblatt, Hyperbolic Flows, Zurich Lectures in Advanced Mathematics, European Mathematical Society Publishing House, 2019.
7 M. Oka, Expansiveness of real flows, Tsukuba J. Math. 14 (1990), no. 1, 1-8. https://doi.org/10.21099/tkbjm/1496161314   DOI
8 A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Encyclopedia of Mathematics and its Applications, 54, Cambridge University Press, Cambridge, 1995. https://doi.org/10.1017/CBO9780511809187   DOI
9 A. Artigue, Kinematic expansive flows, Ergodic Theory Dynam. Systems 36 (2016), no. 2, 390-421. https://doi.org/10.1017/etds.2014.65   DOI
10 R. Bowen and P. Walters, Expansive one-parameter flows, J. Differential Equations 12 (1972), 180-193. https://doi.org/10.1016/0022-0396(72)90013-7   DOI
11 W. Flinn, Expansive flows, PhD thesis, Warwick University, 1972.
12 A. A. Gura, The horocycle flow on a surface of negative curvature is separating, Mat. Zametki 36 (1984), no. 2, 279-284.
13 A. Artigue, Rescaled expansivity and separating flows, Discrete Contin. Dyn. Syst. 38 (2018), no. 9, 4433-4447. https://doi.org/10.3934/dcds.2018193   DOI