n-dimensional transformations and invariant measures

✍ Scribed by M. Mohseni Moghadam; M. Panahi

• Book ID: 104331451
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 270 KB
• Volume: 30
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(97)00359-3

✦ Synopsis

In 1960 Ulam conjectured that it might be possible to construct finite-dimensional operators which approximate P, and whose fixed points approximate the fixed point of P, [l] where r : I" -+ I"

is a piecewise expanding transformation.

In [2,3,4,5] this conjecture was proved for a class of onedimensional piecewise expanding transformations.

Recently the above conjecture was proved for general finite rank operators by indicating an a.rbitrary action matrix [6]. The aim of this paper is to prove a version of Ulam's conjecture in a higher-dimensional setting with a cla.ss of action matrices.