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Deviations in the Franks–Misiurewicz conjecture

Part of: Low-dimensional dynamical systems Topological dynamics

Published online by Cambridge University Press:  26 February 2019

ALEJANDRO PASSEGGI  and
MARTÍN SAMBARINO
ALEJANDRO PASSEGGI
Affiliation:
UdelaR, Facultad de Ciencias, Uruguay email alepasseggi@gmail.com, samba@cmat.edu.uy
MARTÍN SAMBARINO
Affiliation:
UdelaR, Facultad de Ciencias, Uruguay email alepasseggi@gmail.com, samba@cmat.edu.uy
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Abstract

We show that if there exists a counter example for the rational case of the Franks–Misiurewicz conjecture, then it must exhibit unbounded deviations in the complementary direction of its rotation set.

Keywords

Franks–Misiurewicz conjecturerotation theorytopological dynamics

MSC classification

Primary: 37E45: Rotation numbers and vectors
Secondary: 37E30: Homeomorphisms and diffeomorphisms of planes and surfaces 37B45: Continua theory in dynamics
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 40 , Issue 9 , September 2020 , pp. 2533 - 2540
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Copyright
© Cambridge University Press, 2019

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