Dynamics of non abelian affine homotheties group of C^n (1104.2054v1)

Published 11 Apr 2011 in math.DS

Abstract: In this paper we study the action of non abelian subgroup G generated by affine homotheties on C^n. We prove that there exist a subgroup H of C{0}, a G-invariant affine subspace E of Cⁿ and b in E such that the closure of any orbit G(z) is equal to H(z-a)+E, z in C^n. In particular, every orbit in E is dense in it. Moreover, if the complementary U=Cⁿ \E is non empty, every orbit of U is minimal in it.

Abstract PDF Chat (Pro)

Summary

We haven't generated a summary for this paper yet.

Whiteboard

Generate a whiteboard explanation of this paper.

Sign Up to Generate

Paper to Video (Beta)

Generate a video overview of this paper.

Sign Up to Generate

Paper Prompts

Sign up for free to create and run prompts on this paper using GPT-5.

Top Community Prompts

Explain it Like I'm 14

Practical Applications

Conceptual Simplification

Sign Up to Activate View All Prompts

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Continue Learning

We haven't generated follow-up questions for this paper yet.

Authors (2)

Collections

Sign up for free to add this paper to one or more collections.