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Rescaled expansivity and separating flows

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  • In this article we give sufficient conditions for Komuro expansivity to imply the rescaled expansivity recently introduced by Wen and Wen. Also, we show that a flow on a compact metric space is expansive in the sense of Katok-Hasselblatt if and only if it is separating in the sense of Gura and the set of fixed points is open.

    Mathematics Subject Classification: 37B05.


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  • [1] V. AraujoM. J. PacificoE. R. Pujals and M. Viana, Singular-hyperbolic attractors are chaotic, Trans. Amer. Math. Soc., 361 (2009), 2431-2485.  doi: 10.1090/S0002-9947-08-04595-9.
    [2] A. Artigue, Expansive flows of surfaces, Disc. & Cont. Dyn. Sys., 33 (2013), 505-525.  doi: 10.3934/dcds.2013.33.505.
    [3] A. Artigue, Kinematic expansive flows, Ergodic Theory and Dynamical Systems, 36 (2016), 390-421.  doi: 10.1017/etds.2014.65.
    [4] C. Bonatti and A. da Luz, Star Flows and Multisingular Hyperbolicity, arXiv, 2017.
    [5] R. Bowen and P. Walters, Expansive one-parameter flows, J. Diff. Eq., 12 (1972), 180-193.  doi: 10.1016/0022-0396(72)90013-7.
    [6] M. Brunella, Expansive flows on Seifert manifolds and torus bundles, Bol. Soc. Bras. Mat., 24 (1993), 89-104. 
    [7] W. Cordeiro, Fluxos CW-expansivos, Phd Thesis, UFRJ, Brazil, 2015.
    [8] M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, Inc. Englewood Cliffs, New Jersey, 1976.
    [9] L. W. Flinn, Expansive Flows, Phd Thesis, University of Warwick, 1972.
    [10] A. A. Gura, Horocycle flow on a surface of negative curvature is separating, Mat. Zametki, 36 (1984), 279-284. 
    [11] U. Hamenstadt, Dynamics of the Teichmuller flow on compact invariant sets, J. Mod. Dyn., 4 (2010), 393-418.  doi: 10.3934/jmd.2010.4.393.
    [12] T. Inaba and S. Matsumoto, Nonsingular expansive flows on 3-manifolds and foliations with circle prong singularities, Japan. J. Math., 16 (1990), 329-340.  doi: 10.4099/math1924.16.329.
    [13] A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, 1995. doi: 10.1017/CBO9780511809187.
    [14] H. Keynes and M. Sears, Real-expansive flows and topological dimension, Ergodic Theory and Dynamical Systems, 1 (1981), 179-195. 
    [15] M. Komuro, Expansive properties of Lorenz attractors, The Theory of Dynamical Systems and Its Applications to Nonlinear Problems, World Sci. Singapure, Kyoto, (1984), 4-26.
    [16] K. MoriyasuK. Sakai and W. Sun, $C^1$-stably expansive flows, Journal of Differential Equations, 213 (2005), 352-367.  doi: 10.1016/j.jde.2004.08.003.
    [17] M. Paternain, Expansive flows and the fundamental group, Bull. Braz. Math. Soc., 24 (1993), 179-199. 
    [18] X. Wen and L. Wen, A Rescaled Expansiveness for Flows, arXiv, 2017.
    [19] X. Wen and Y. Yu, Equivalent definitions of rescaled expansiveness, J. Korean Math. Soc., 55 (2018), 593-604. 
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