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 - - dxk + ez) where a, b, c, d, e are real parameters with bd ≠ 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.
Original language | English |
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Pages (from-to) | 181-190 |
Number of pages | 10 |
Journal | Regular and Chaotic Dynamics |
Volume | 11 |
Issue number | 2 |
DOIs | |
State | Published - 7 Jul 2006 |
Keywords
- Full shift
- Generalized Hénon maps
- Inverse limit
- Nonwandering set
- Polynomial maps
- Topological entropy
- Topological horseshoe