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Existence and stability of traveling waves for Leslie-Gower predator-prey system with nonlocal diffusion
Constructing attracting cycles for Halley and Schröder maps of polynomials
Department of Mathematics and Computer Science, Freed-Hardeman University, Henderson, TN 38340, USA |
We show that for any set of $n$ distinct points in the complex plane, there exists a polynomial $p$ of degree at most $n+1$ so that the corresponding Halley and Schröder map for $p$ has the given points as a super-attracting cycle. This improves the result in [
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A construction of attracting periodic orbits for some classical third-order iterative methods, J. Comput. Appl. Math., 189 (2006), 22-33.
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Specifying attracting cycles for Newton maps of polynomials, J. Difference Equ. Appl., 19 (2013), 1361-1379.
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Julia sets for the super-Newton method, Cauchy's method and Halley's method, Chaos, 11 (2001), 359-370.
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S. Plaza and N. Romero,
Attracting cycles for the relaxed Newton's method, J. Comput. Appl. Math., 235 (2011), 3238-3244.
doi: 10.1016/j.cam.2011.01.010. |
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S. Plaza and V. Vergara,
Existence of attracting periodic orbits for the Newton method, Sci. Ser. A Math. Sci., 7 (2001), 31-36.
|
show all references
References:
| [1] |
S. Amat, S. Busquier and S. Plaza,
A construction of attracting periodic orbits for some classical third-order iterative methods, J. Comput. Appl. Math., 189 (2006), 22-33.
doi: 10.1016/j.cam.2005.03.049. |
| [2] |
J. Campbell and J. Collins,
Specifying attracting cycles for Newton maps of polynomials, J. Difference Equ. Appl., 19 (2013), 1361-1379.
doi: 10.1080/10236198.2012.751987. |
| [3] |
D. Hilbert,
Über die vollen Invariantensysteme, Math. Ann., 42 (1893), 313-373.
doi: 10.1007/BF01444162. |
| [4] |
K. Kneisl,
Julia sets for the super-Newton method, Cauchy's method and Halley's method, Chaos, 11 (2001), 359-370.
doi: 10.1063/1.1368137. |
| [5] |
S. Plaza and N. Romero,
Attracting cycles for the relaxed Newton's method, J. Comput. Appl. Math., 235 (2011), 3238-3244.
doi: 10.1016/j.cam.2011.01.010. |
| [6] |
S. Plaza and V. Vergara,
Existence of attracting periodic orbits for the Newton method, Sci. Ser. A Math. Sci., 7 (2001), 31-36.
|
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