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) |
|---|---|
| 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
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Kan, I., Koçak, H., & Yorke, J. A. (1995). Persistent homoclinic tangencies in the Hénon family. Physica D: Nonlinear Phenomena, 83(4), 313-325. https://doi.org/10.1016/0167-2789(94)00226-G