63 citations · 295 across the 47 of their papers we have counts for
6 papers · 1 filter
On dynamics of the Sierpiński carpet
Jan P. Boroński, P. Oprocha
We prove that the Sierpiński curve admits a homeomorphism with strong mixing properties. We also prove that the constructed example does not have Bowen's specification property.
On the irregular points for systems with the shadowing property
Yiwei Dong, Piotr Oprocha, Xueting Tian
We prove that when is a continuous selfmap acting on compact metric space which satisfies the shadowing property, then the set of irregular points (i.e. points with div…
When all closed subsets are recurrent?
Jie Li, Piotr Oprocha, Xiangdong Ye +1
In the paper we study relations of rigidity, equicontinuity and pointwise recurrence between a t.d.s. and the t.d.s. induced on the hyperspace of all co…
Mixing properties in coded systems
Jeremias Epperlein, Dominik Kwietniak, Piotr Oprocha
We show that topological mixing, weak mixing and total transitivity are equivalent for coded systems. We provide an example of a mixing coded system which cannot be approximated by…
A panorama of specification-like properties and their consequences
Dominik Kwietniak, Martha Łącka, Piotr Oprocha
We offer an overview of the specification property, its relatives and their consequences. We examine relations between specification-like properties and such notions as: mixing, en…
Multi-recurrence and van der Waerden systems
Dominik Kwietniak, Jian Li, Piotr Oprocha +1
We explore recurrence properties arising from dynamical approach to combinatorial problems like the van der Waerden Theorem. We describe relations between these properties, study t…