publication . Article . Other literature type . 1979

Shift automorphisms in the Hénon mapping

Devaney, R.; Nitecki, Z.;
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  • Published: 01 Jun 1979 Journal: Communications in Mathematical Physics, volume 67, pages 137-146 (issn: 0010-3616, eissn: 1432-0916, Copyright policy)
  • Publisher: Springer Science and Business Media LLC
Abstract
We investigate the global behavior of the quadratic diffeomorphism of the plane given byH(x,y)=(1+y−Ax2,Bx). Numerical work by Henon, Curry, and Feit indicate that, for certain values of the parameters, this mapping admits a “strange attractor”. Here we show that, forA small enough, all points in the plane eventually move to infinity under iteration ofH. On the other hand, whenA is large enough, the nonwandering set ofH is topologically conjugate to the shift automorphism on two symbols.
Subjects
arXiv: Mathematics::Dynamical Systems
free text keywords: Mathematical Physics, Statistical and Nonlinear Physics, Automorphism, Attractor, Nonlinear system, Quadratic equation, Topology, Topological conjugacy, Infinity, media_common.quotation_subject, media_common, Mathematics, Quantum computer, Diffeomorphism, Mathematical analysis, 58F15, 58F13
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