4 papers
Lift-Free Approaches to Random Rotation Number and Numerical Approximation
Zixu Li, Simon Lloyd
We study the random rotation number for random circle homeomorphisms. We introduce two new definitions of the random rotation number that can be stated without reference to any cho…
Periodicity and Rotation Number for Random Circle Homeomorphisms
Zixu Li, Simon Lloyd
We study discrete-time random dynamical systems where each fibre map is an orientation-preserving homeomorphism of the circle. We prove that the existence of a random periodic cycl…
A cluster theory approach from mutation invariants to Diophantine equations
Zhichao Chen, Zixu Li
In this paper, we define and classify the sign-equivalent exchange matrices. We give a Diophantine explanation for the differences between rank 2 cluster algebras of finite type an…
Mutation invariants of cluster algebras of rank 2
Zhichao Chen, Zixu Li
We consider the mutation invariants of cluster algebras of rank 2. We characterize the mutation invariants of finite type. Two examples are provided for the affine type and we prov…