Holomorphic symplectomorphisms in \(\mathbb{C}^{2p}\)
type: Item
instance of: scholarly article
title: Holomorphic symplectomorphisms in \(\mathbb{C}^{2p}\)
zbMATH Open document ID: 0871.57031
DOI: 10.1215/S0012-7094-96-08213-7
author: Nessim Sibony
author: J. E. Fornæss
published in: Duke Mathematical Journal
publication date: 1997-10-08T00:00:00Z
review text: The authors study the properties of biholomorphic symplectomorphisms of \(\mathbb{C}^{2p}\), mainly the structure of the space of periodic or quasi-periodic orbits. They show that for the time-independent holomorphic Hamiltonians in \(\mathbb{C}^{2p}\), generically all orbits of the corresponding biholomorphic symplectomorphisms go to infinity. They also confirm Herman's conjecture, i.e. that there is a \(G_\delta\) dense set \(S'\) of the space of biholomorphic symplectomorphisms of \(\mathbb{C}^{2p}\) (endowed with the topology of uniform convergence on compact sets) such that for \(f\in S'\) the set \(\{(z, w);\;f^n(z,w)\) is bounded\} has empty interior.
Mathematics Subject Classification ID: 32H50
Mathematics Subject Classification ID: 37F50
Mathematics Subject Classification ID: 37J10
zbMATH DE Number: 908691
zbMATH Keywords: Hamiltonian flows
zbMATH Keywords: Fatou sets
zbMATH Keywords: biholomorphic symplectomorphisms
reviewed by: Stanisław Janeczko
MaRDI profile type: Publication
cites work: Volume-preserving automorphisms of C⊃n⊃
cites work: Q4166257
cites work: Q4868370
cites work: Uniform Approximation on Compact Sets in $\mathsf{C}^n$.
cites work: Q5628476
full work available at URL: s0012-7094-96-08213-7
OpenAlex ID: W1982834762
description: scientific article; zbMATH DE number 908691