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A solution to Flinn’s conjecture on weakly expansive flows

Part of: Dynamical systems with hyperbolic behavior Low-dimensional dynamical systems

Published online by Cambridge University Press:  26 February 2020

HIEN MINH HUYNH
HIEN MINH HUYNH*
Affiliation:
Department of Mathematics and Statistics, Quy Nhon University, 170 An Duong Vuong, Quy Nhon, Vietnam email huynhminhhien@qnu.edu.vn
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Abstract

In L. W. Flinn’s PhD thesis published in 1972, the author conjectured that weakly expansive flows are also expansive flows. In this paper we use the horocycle flow on compact Riemann surfaces of constant negative curvature to show that Flinn’s conjecture is not true.

Keywords

horocycle flowweakly expansivestrong kinematic expansiveFlinn’s conjecture

MSC classification

Primary: 37D40: Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
Secondary: 37E35: Flows on surfaces
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 5 , May 2021 , pp. 1390 - 1396
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Copyright
© The Author(s) 2020. Published by Cambridge University Press

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