Dynamics of biholomorphic self-maps on bounded symmetric domains
|Title:||Dynamics of biholomorphic self-maps on bounded symmetric domains||Authors:||Mellon, Pauline||Permanent link:||http://hdl.handle.net/10197/9323||Date:||2015||Abstract:||Let g be a fixed-point free biholomorphic self-map of a bounded symmetric domain B. It is known that the sequence of iterates (gn) may not always converge locally uniformly on B even, for example, if B is an infinite dimensional Hilbert ball. However, g=ga∘T, for a linear isometry T, a=g(0) and a transvection ga, and we show that it is possible to determine the dynamics of ga. We prove that the sequence of iterates (gna) converges locally uniformly on B if, and only if, a is regular, in which case, the limit is a holomorphic map of B onto a boundary component (surprisingly though, generally not the boundary component of a∥a∥). We prove (gna) converges to a constant for all non-zero a if, and only if, B is a complex Hilbert ball. The results are new even in finite dimensions where every element is regular.||Type of material:||Journal Article||Publisher:||Royal Danish Library||Keywords:||Complex Hilbert spaces;Complex Banach spaces;Regular elements||DOI:||10.7146/math.scand.a-22867||Language:||en||Status of Item:||Peer reviewed|
|Appears in Collections:||Mathematics and Statistics Research Collection|
Show full item record
This item is available under the Attribution-NonCommercial-NoDerivs 3.0 Ireland. No item may be reproduced for commercial purposes. For other possible restrictions on use please refer to the publisher's URL where this is made available, or to notes contained in the item itself. Other terms may apply.