Abstract
Homoclinic tangencies in the Hénon family fθ{symbol} (x, y) = (λ - x2 + by, x) for the parameter values b = 0.3 and λ ε{lunate} [1.270, 1.420] are investigated. Our main observation is that there exist three intervals comprising 93 percent of the values of the parameter λ such that for a dense set of parameter values in these intervals the Hénon family possesses a homoclinic tangency. Therefore, one should expect long parameter intervals where the Hénon family is not structurally stable. Strong numerical support for this observation is provided.
Original language | English (US) |
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Pages (from-to) | 313-325 |
Number of pages | 13 |
Journal | Physica D: Nonlinear Phenomena |
Volume | 83 |
Issue number | 4 |
DOIs | |
State | Published - Jun 1 1995 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics