arXiv subjects

G. Soler López

Publications and source records attributed to G. Soler López.

3 recordsLinked to original sources

arXiv2020

Minimal non uniquely ergodic flipped IETs

In this paper we prove the existence of minimal non uniquely ergodic flipped IETs. In particular, we build explicitly minimal non uniquely ergodic $(10,k)$-IETs for any $1\leq k \leq 10$. This answers an open question posed in [C.~Gutierrez, S.~Lloyd, V.~Medvedev, B.~Pires, and E.~Zhuzhoma.Transitive circle exchange transformations with flips. Discrete Contin. Dyn. Syst.,26 (1):251--263, 2010]. As a consequence, we also derive the existence of transitive non uniquely ergodic $(n,k)$-IETs, for any $n\geq 10$ and $1\leq k\leq n$ if $n$ is even, and $1\leq k\leq n-1$ if $n$ is odd.

nlin.CD↗

arXiv2019

Computing odd periods of alternating systems of affine circle maps

Let $f,g$ be affine circle maps and let $[f,g]$ be the alternating system generated by $f$ and $g$. We present an algorithm to compute the periodic structure of $[f,g]$.

nlin.CD↗

arXiv2017

Existence of minimal flows on nonorientable surfaces

Surfaces admitting flows all whose orbits are dense are called minimal. Minimal orientable surfaces were characterized by J.C. Benière in 1998, leaving open the nonorientable case. This paper fills this gap providing a characterization of minimal nonorientable surfaces of finite genus. We also construct an example of a minimal nonorientable surface with infinite genus and conjecture that any nonorientable surface without combinatorial boundary is minimal.

math.DS↗