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Kinematic expansive flows

Published online by Cambridge University Press:  05 August 2014

ALFONSO ARTIGUE
ALFONSO ARTIGUE*
Affiliation:
DMEL, Regional Norte, Universidad de la República, Gral. Rivera 1350, Salto, Uruguay email [email protected]
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Abstract

In this paper we study kinematic expansive flows on compact metric spaces, surfaces and general manifolds. Different variations of the definition are considered and its relationship with expansiveness in the sense of Bowen–Walters and Komuro is analyzed. We consider continuous and smooth flows and robust kinematic expansiveness of vector fields is considered on smooth manifolds.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 2 , April 2016 , pp. 390 - 421
Copyright
© Cambridge University Press, 2014 

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References

Artigue, A.. Expansive flows of surfaces. Discrete Contin. Dyn. Syst. 33 (2013), 505–525.CrossRefGoogle Scholar
Artigue, A.. Positive expansive flows. Topology Appl. 165 (2014), 121–132.CrossRefGoogle Scholar
Avila, A. and Kocsard, A.. Cohomological equations and invariant distributions for minimal circle diffeomorphisms. Duke Math. J. 158(3) (2011), 501–536.CrossRefGoogle Scholar
Baker, G. L. and Blackburn, J. A.. The Pendulum: A Case Study in Physics. Oxford University Press, Oxford, 2005.CrossRefGoogle Scholar
Bowen, R. and Walters, P.. Expansive one-parameter flows. J. Differential Equations 12 (1972), 180–193.CrossRefGoogle Scholar
Cerminara, M. and Lewowicz, J.. Some open problems concerning expansive systems. Rend. Istit. Mat. Univ. Trieste 42 (2010), 129–141.Google Scholar
DeStefano, A. and Hall, G. R.. An example of a universally observable flow on the torus. SIAM J. Control Optim. 36(4) (1998), 1207–1224.CrossRefGoogle Scholar
Gan, S. and Wen, L.. Nonsingular star flows satisfy Axiom A and the no-cycle condition. Invent. Math. 164 (2006), 279–315.CrossRefGoogle Scholar
Gura, A. A.. Separating diffeomorphisms of the torus. Mat. Zametki 18 (1975), 41–49.Google Scholar
Gura, A. A.. Horocycle flow on a surface of negative curvature is separating. Mat. Zametki 36 (1984), 279–284.Google Scholar
Gutierrez, C.. Smoothing continuous flows on two-manifolds and recurrences. Ergod. Th. & Dynam. Sys. 6 (1986), 14–44.CrossRefGoogle Scholar
Hartman, P.. Ordinary Differential Equations. John Wiley & Sons Inc., New York, 1964.Google Scholar
Keynes, H. B. and Sears, M.. F-expansive transformation group. Gen. Topology Appl. (1979), 67–85.CrossRefGoogle Scholar
Keynes, H. B. and Sears, M.. Real-expansive flows and topological dimension. Ergod. Th. & Dynam. Sys. 1 (1981), 179–195.CrossRefGoogle Scholar
Komuro, M.. Expansive properties of Lorenz attractors. The Theory of Dynamical Systems and its Applications to Nonlinear Problems. World Scientific, Singapore, 1984, pp. 4–26.Google Scholar
Moriyasu, K., Sakai, K. and Sun, W.. C 1 -stably expansive flows. J. Differential Equations 213 (2005), 352–367.CrossRefGoogle Scholar
Peixoto, M. M.. Structural stability on two-dimensional manifolds. Topology 1 (1962), 101–120.CrossRefGoogle Scholar
Rudin, M. E.. A topological characterization of sets of real numbers. Pacific J. Math. 7(2) (1957), 1185–1186.CrossRefGoogle Scholar
Whitney, H.. Regular family of curves. Ann. of Math. (2) 34 (1933), 244–270.CrossRefGoogle Scholar