A COMBINATORIAL PROCEDURE FOR FINDING ISOLATING NEIGHBORHOODS AND INDEX PAIRS

Authors
SZYMCZAK A
Citation
A. Szymczak, A COMBINATORIAL PROCEDURE FOR FINDING ISOLATING NEIGHBORHOODS AND INDEX PAIRS, Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, 127, 1997, pp. 1075-1088
Citations number
10
Categorie Soggetti
Mathematics, General",Mathematics,Mathematics
Journal title
Proceedings of the Royal Society of Edinburgh. Section A. Mathematics → ACNP
ISSN journal
03082105
Volume
127
Year of publication
1997
Part
5
Pages
1075 - 1088
Database
ISI
SICI code
0308-2105(1997)127:<1075:ACPFFI>2.0.ZU;2-J
Abstract
We present a purely combinatorial procedure for finding an isolating n eighbourhood and an index pair contained in a given set, being a finit e union of cubes in R-s. It is applied for a computer-assisted computa tion of the Conley index of an isolated invariant subset of the Henon attractor. As a corollary, it is shown that the Henon attractor contai ns periodic orbits of all principal periods except for 3 and 5.