INFINITE-DIMENSIONAL JACOBI MATRICES ASSOCIATED WITH JULIA SETS

@inproceedings{Barnsley1983INFINITEDIMENSIONALJM,
  title={INFINITE-DIMENSIONAL JACOBI MATRICES ASSOCIATED WITH JULIA SETS},
  author={Michael F. Barnsley and Jeffrey S. Geronimo and A. N. Harrington},
  year={1983}
}
Let B be the Julia set associated with the polynomial Tz = z N + kiz s ~ ' + •■ ■ +A v. and let ii be the balanced T-invariant measure on B. Assuming B is totally real, we give relations among the entries in the infinite-dimensional Jacobi matrix J whose spectral measure is ii. The specific example Tz = r' — Xz is given, and some of the asymptotic properties of the entries in J are presented. capacity, and on it can be placed an equilibrium charge distribution p. This provides a measure on B… CONTINUE READING