Fractal basin boundary in dynamical systems and the Weierstrass-Takagi functions |
| |
| Institution: | 1. Department of Anesthesia, Critical Care and Pain Medicine, Massachusetts General Hospital, Boston, MA, USA;2. Harvard Medical School, Boston, MA, USA;3. Department of Anesthesia, Brigham & Women''s Hospital, Boston, MA, USA;4. STRATUS Center for Medical Simulation, Brigham & Women''s Hospital, Boston, MA, USA;5. Center for Medical Simulation, Charlestown, MA, USA |
| |
| Abstract: | It is shown that the basin boundary of the complex maps Zn+1 = Zqn + C (q⩾2 is an integer and |C| ⪡ 1) is expressible with the Weierstrass function which is continuous but nowhere differentiable. The relation between the Weierstrass function and the Takagi function is discussed, and these functions are extended in a general situation. The fractal basin boundaries expressed by the generalized Weierstrass-Takagi functions are investigated. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
