  Chebyshev polynomials in one variable are typical chaotic maps on the complex
1-space. Chebyshev endomorphisms f on the complex n-space A are also chaotic.
The endomorphisms f induce mappings on the quotient space A/G, where G is the
dihedral group of order 2(n+1). Using invariant theory we embed A/G as an
affine subvariety X in the complex m-space. Then we have morphisms g on X.
  We study the chaotic properties of g when n = 2 and 3.
