Transitive endomorphisms with critical points

Ranter, Wagner

doi:10.1090/proc/13737

Transitive endomorphisms with critical points
HTML articles powered by AMS MathViewer

by Wagner Ranter

Proc. Amer. Math. Soc. 146 (2018), 125-136

DOI: https://doi.org/10.1090/proc/13737

Published electronically: October 6, 2017

PDF | Request permission

Abstract:

We show that a non-wandering endomorphism on the torus with topological degree at least two, hyperbolic linear part, and for which the critical points are in some sense “generic” is transitive. This is an improvement of a result by Andersson (Nonlinearity 29 (2016), 1047), since it allows critical points and relaxes the volume preserving hypothesis.

References

N. Aoki and K. Hiraide, Topological theory of dynamical systems, North-Holland Mathematical Library, vol. 52, North-Holland Publishing Co., Amsterdam, 1994. Recent advances. MR 1289410
Martin Andersson, Transitivity of conservative toral endomorphisms, Nonlinearity 29 (2016), no. 3, 1047–1055. MR 3465993, DOI 10.1088/0951-7715/29/3/1047
William S. Massey, Algebraic topology: an introduction, Graduate Texts in Mathematics, Vol. 56, Springer-Verlag, New York-Heidelberg, 1977. Reprint of the 1967 edition. MR 0448331
M. Shub, Dynamical systems, filtrations and entropy, Bull. Amer. Math. Soc. 80 (1974), 27–41. MR 334284, DOI 10.1090/S0002-9904-1974-13344-6
Hassler Whitney, On singularities of mappings of euclidean spaces. I. Mappings of the plane into the plane, Ann. of Math. (2) 62 (1955), 374–410. MR 73980, DOI 10.2307/1970070