14 citations · 17 across the 16 of their papers we have counts for
7 papers · 1 filter
Minimal sets for torus homeomorphisms with an irrational circle factor
Xiao-Chuan Liu
We study minimal sets of torus homeomorphisms admitting an irrational circle factor whose fibres are thin essential annular continua. For totally irrational pseudo-rotations and ho…
On Non-contractible Periodic Orbits and Bounded Deviations
Xiao-Chuan Liu, Fabio Armando Tal
We present a dichotomy for surface homeomorphisms in the isotopy class of the identity. We show that, in the absence of a degenerate fixed point set, either there exists a uniform…
Uniform convergence rate for Birkhoff means of certain uniquely ergodic toral maps
Silvius Klein, Xiao-Chuan Liu, Aline Melo
We obtain estimates on the uniform convergence rate of the Birkhoff average of a continuous observable over torus translations and affine skew product toral transformations. The co…
Prime Ends Dynamics in Parametrised Families of Rotational Attractors
Jan P. Boroński, Jernej Činč, Xiao-Chuan Liu
We provide several new examples in dynamics on the -sphere, with the emphasis on better understanding the induced boundary dynamics of invariant domains in parametrized families…
On Stable and Unstable Behaviours of Certain Rotation Segments
Salvador Addas-Zanata, Xiao-Chuan Liu
In this paper, we study non-wandering homeomorphisms of the two torus in the identity homotopy class, whose rotation sets are non-trivial line segments from to some totally…
Minimal non-invertible maps on the pseudo-circle
Jan P. Boronski, Judy Kennedy, Xiao-Chuan Liu +1
In this article, we show that R.H. Bing's pseudo-circle admits a minimal non-invertible map. This resolves a problem raised by Bruin, Kolyada and Snoha in the negative. The main to…
Livsic theorem for diffeomorphism cocycles
Artur Avila, Alejandro Kocsard, Xiao-Chuan Liu
We prove the so called Livšic theorem for cocycles taking values in the group of $C^{1+β}-diffeomorphisms of any closed manifold of arbitrary dimension. Since no localization hypot…