Geodesic
On sectional Newtonian graphs
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 3, pp. 605-629

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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.
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.
DOI : 10.21136/CMJ.2020.0049-20
Classification : 05C75, 53C43
Keywords: sectional Newtonian graph; level set; partition 
Fan, Zening; Zhao, Suo. On sectional Newtonian graphs. Czechoslovak Mathematical Journal, Tome 70 (2020) no. 3, pp. 605-629. doi: 10.21136/CMJ.2020.0049-20
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[1] Duren, P.: Harmonic Mappings in the Plane. Cambridge Tracts in Mathematics 156. Cambridge University Press, Cambridge (2004). | DOI | MR | JFM

[2] Griffths, P., Harris, J.: Principles of Algebraic Geometry. Wiley Classics Library. John Wiley & Sons, New York (1994). | DOI | MR | JFM

[3] Huybrechts, D.: Complex Geometry: An Introduction. Universitext. Springer, Berlin (2005). | DOI | MR | JFM

[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. | DOI | MR | JFM

[5] Kahn, J.: Newtonian graphs for families of complex polynomials. J. Complexity 7 (1991), 425-442. | DOI | MR | JFM

[6] Kozen, D., Stefánsson, K.: Computing the Newtonian graph. J. Symb. Comput. 24 (1997), 125-136. | DOI | MR | JFM

[7] Shub, M., Tischler, D., Williams, R. F.: The Newtonian graph of a complex polynomial. SIAM J. Math. Anal. 19 (1988), 246-256. | DOI | MR | JFM

[8] Smale, S.: On the efficiency of algorithms of analysis. Bull. Am. Math. Soc., New Ser. 13 (1985), 87-121. | DOI | MR | JFM

[9] Stefánsson, K.: Newtonian Graphs, Riemann Surfaces and Computation. PhD Thesis. Cornell University, Ann Arbor (1995). | MR

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