| Title:
|
On sectional Newtonian graphs (English) |
| Author:
|
Fan, Zening |
| Author:
|
Zhao, Suo |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
70 |
| Issue:
|
3 |
| Year:
|
2020 |
| Pages:
|
605-629 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we introduce the so-called sectional Newtonian graphs for univariate complex polynomials, and study some properties of those graphs. In particular, we list all possible sectional Newtonian graphs when the degrees of the polynomials are less than five, and also show that every stable gradient graph can be realized as a polynomial sectional Newtonian graph. (English) |
| Keyword:
|
sectional Newtonian graph |
| Keyword:
|
level set |
| Keyword:
|
partition |
| MSC:
|
05C75 |
| MSC:
|
53C43 |
| idZBL:
|
07250679 |
| idMR:
|
MR4151695 |
| DOI:
|
10.21136/CMJ.2020.0049-20 |
| . |
| Date available:
|
2020-09-07T09:33:45Z |
| Last updated:
|
2022-10-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148317 |
| . |
| Reference:
|
[1] Duren, P.: Harmonic Mappings in the Plane.Cambridge Tracts in Mathematics 156. Cambridge University Press, Cambridge (2004). Zbl 1055.31001, MR 2048384, 10.1017/CBO9780511546600 |
| Reference:
|
[2] Griffths, P., Harris, J.: Principles of Algebraic Geometry.Wiley Classics Library. John Wiley & Sons, New York (1994). Zbl 0836.14001, MR 1288523, 10.1002/9781118032527 |
| Reference:
|
[3] Huybrechts, D.: Complex Geometry: An Introduction.Universitext. Springer, Berlin (2005). Zbl 1055.14001, MR 2093043, 10.1007/b137952 |
| Reference:
|
[4] Jongen, H. T., Jonker, P., Twilt, F.: On the classification of plane graphs representing structurally stable rational Newton flows.J. Comb. Theory, Ser. B 51 (1991), 256-270. Zbl 0725.05069, MR 1099075, 10.1016/0095-8956(91)90041-H |
| Reference:
|
[5] Kahn, J.: Newtonian graphs for families of complex polynomials.J. Complexity 7 (1991), 425-442. Zbl 0773.05055, MR 1143970, 10.1016/0885-064X(91)90029-W |
| Reference:
|
[6] Kozen, D., Stefánsson, K.: Computing the Newtonian graph.J. Symb. Comput. 24 (1997), 125-136. Zbl 0885.65055, MR 1476256, 10.1006/jsco.1997.0118 |
| Reference:
|
[7] Shub, M., Tischler, D., Williams, R. F.: The Newtonian graph of a complex polynomial.SIAM J. Math. Anal. 19 (1988), 246-256. Zbl 0653.58013, MR 0924558, 10.1137/0519018 |
| Reference:
|
[8] Smale, S.: On the efficiency of algorithms of analysis.Bull. Am. Math. Soc., New Ser. 13 (1985), 87-121. Zbl 0592.65032, MR 0799791, 10.1090/S0273-0979-1985-15391-1 |
| Reference:
|
[9] Stefánsson, K.: Newtonian Graphs, Riemann Surfaces and Computation. PhD Thesis.Cornell University, Ann Arbor (1995). MR 2693724 |
| . |
