On Holomorphic Maps Which Commute with Hyperbolic Automorphisms

Hyperbolic Automorphisms and Holomorphic Motions in C 2

Holomorphic motions have been an important tool in the study of complex dynamics in one variable. In this paper we provide one approach to using holomorphic motions in the study of complex dynamics in two variables. To introduce these ideas more fully, let 1r be the disk of radius r and center 0 in the plane, let P1 be the Riemann sphere, and recall that a holomorphic motion of a set E ⊂ P1 is ...

Multiplicative Maps on Ideals of Operators Which Are Local Automorphisms

We present the following reflexivity-like result concerning the automorphism group of the C∗-algebra B(H), H being a separable Hilbert space. Let φ : B(H) → B(H) be a multiplicative map (no linearity or continuity is assumed) which can be approximated at every point by automorphisms of B(H) (these automorphisms may, of course, depend on the point) in the operator norm. Then φ is an automorphism...

Holomorphic Maps for Which the Unstable Manifolds 737

Commutators Which Commute with One Factor

Let A and B be n × n matrices, let C = ABA−1B−1 be the multiplicative commutator of A and B, and assume AC = CA. Olga Taussky (1961) examined the structure of A and B for the case where A and B are unitary. Marcus and Thompson (1966) generalized her results to the case where A and C are assumed normal. We look at this problem for general A, with particular attention to the cases where A is diag...

Hyperbolic Automorphisms and Anosov Diffeomorphisms on Nilmanifolds

We translate the problem of finding Anosov diffeomorphisms on a nilmanifold which is covered by a free nilpotent Lie group into a problem of constructing matrices in GL(n,Z) whose eigenvalues satisfy certain conditions. Afterwards, we show how this translation can then be solved in some specific situations. The paper starts with a section on polynomial permutations of QK , a subject which is of...