Topological classification of affine operators on unitary and Euclidean spaces

TL;DR

This paper provides a topological classification of affine operators on unitary and Euclidean spaces, identifying when two such operators are equivalent under homeomorphisms.

Contribution

It introduces a comprehensive classification scheme for affine operators based on topological conjugacy in Euclidean and unitary spaces.

Findings

Complete classification criteria for affine operators

Identification of invariants under topological conjugacy

Framework applicable to both Euclidean and unitary spaces

Abstract

We classify affine operators on a unitary or Euclidean space U up to topological conjugacy. An affine operator is a map f: U-->U of the form f(x)=Ax+b, in which A: U-->U is a linear operator and b in U. Two affine operators f and g are said to be topologically conjugate if hg=fh for some homeomorphism h: U-->U.