Groups of Real Analytic Diffeomorphisms of the Circle with a Finite Image under the Rotation Number Function
نویسنده
چکیده
We consider groups of orientation-preserving real analytic diffeomorphisms of the circle which have a finite image under the rotation number function. We show that if such a group is nondiscrete with respect to the C-topology then it has a finite orbit. As a corollary, we show that if such a group has no finite orbit then each of its subgroups contains either a cyclic group of finite index or a nonabelian free subgroup.
منابع مشابه
On the numerical computation of Diophantine rotation numbers of analytic circle maps
In this paper we present a numerical method to compute Diophantine rotation numbers of circle maps with high accuracy. We mainly focus on analytic circle diffeomorphisms, but the method also works in the case of (enough) finite differentiability. The keystone of the method is that, under these conditions, the map is conjugate to a rigid rotation of the circle. Moreover, albeit it is not fully j...
متن کاملEuler-Lagrange equations and geometric mechanics on Lie groups with potential
Abstract. Let G be a Banach Lie group modeled on the Banach space, possibly infinite dimensional, E. In this paper first we introduce Euler-Lagrange equations on the Lie group G with potential and right invariant metric. Euler-Lagrange equations are natural extensions of the geodesic equations on manifolds and Lie groups. In the second part, we study the geometry of the mechanical system of a r...
متن کاملComputation of derivatives of the rotation number for parametric families of circle diffeomorphisms
In this paper we present a numerical method to compute derivatives of the rotation number for parametric families of circle diffeomorphisms with high accuracy. Our methodology is an extension of a recently developed approach to compute rotation numbers based on suitable averages of iterates of the map and Richardson extrapolation. We focus on analytic circle diffeomorphisms, but the method also...
متن کاملRotation number and its properties for iterated function and non-autonomous systems
The main purpose of this paper is to introduce the rotation number for non-autonomous and iterated function systems. First, we define iterated function systems and the lift of these types of systems on the unit circle. In the following, we define the rotation number and investigate the conditions of existence and uniqueness of this number for our systems. Then, the notions rotational entropy an...
متن کاملGlobal Rigidity of Solvable Group Actions on S Lizzie Burslem and Amie Wilkinson
In this paper we find all solvable groups that act effectively on the circle as realanalytic diffeomorphisms, and we find all of their actions. Our starting point is the procedure of ramified lifting of group actions with a global fixed point, which we develop in Section 1. To summarize the discussion there, we say that a real analytic map π : S → S is a ramified covering map over p ∈ S if the ...
متن کامل