Abstract
Recently, the authors proved in [C. Lizana and W. Ranter, Topological obstructions for robustly transitive endomorphisms on surfaces, Adv. Math. 390 (2021), pp. 107901] that every -robustly transitive toral endomorphism displaying critical points must be homotopic to a linear endomorphism having at least one eigenvalue with modulus greater than one. Here, we exhibit some examples of
-robustly transitive surface endomorphisms displaying critical points in certain homotopy classes.
Acknowledgments
The authors are grateful to E. Pujals and R. Potrie for insightful comments to improve this work. The authors would like to thank to UFBA, UFAL and ICTP for the nice enviroment and support during the preparation of this work. The authors are grateful to the anonymous referees for helpful comments to improve our paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Notes
1 is the local unstable manifold defined by the set of points
such that there exists a full orbit
with
and
for all
, where
is a full orbit of
and R>0 is locally constant for G. For further details see [Citation13].