On Pseudospectra of Matrix Polynomials and their Boundaries
  In the first part of this paper, the main concern is with smoothness properties of the boundary of the pseudospectrum of a matrix polynomial. In the second part, results are obtained concerning the number of connected components of pseudospectra, as well as results concerning matrix polynomials with multiple eigenvalues, or the proximity to such polynomials. 
Lyonell Boulton, Peter Lancaster and Panayiotis Psarrakos