Title: Topological horseshoes for Arneodo-Coullet-Tresser maps
Authors: Du, BS
Li, MC
Malkin, MI
Department of Applied Mathematics
Keywords: topological horseshoe;full shift;polynomial maps;generalized Henon maps;nonwandering set;inverse limit;topological entropy
Issue Date: 2006
Abstract: In this paper, we study the family of Arneodo-Coullet-Tresser maps F(x, y, z) = (ax - b(y - z), bx + a(y - z), cx - dx(k) + ez) where a, b, c, d, e are real parameters with bd not equal 0 and k > 1 is an integer. We find regions of parameters near anti-integrable limits and near singularities for which there exist hyperbolic invariant sets such that the restriction of F to these sets is conjugate to the full shift on two or three symbols.
URI: http://hdl.handle.net/11536/12875
ISSN: 1560-3547
DOI: 10.1111/j.1365-2052.2006.01427.x
Volume: 11
Issue: 2
Begin Page: 181
End Page: 190
Appears in Collections:Conferences Paper