Geodesic
One-dimensional polynomial maps, periodic points and multipliers
Izvestiya. Mathematics, Tome 77 (2013) no. 4, pp. 700-713 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We discuss tangent maps related to the multipliers of periodic points of a typical one-dimensional polynomial map.
Keywords: complex polynomials in one variable, periodic points
Mots-clés : tangent maps, multipliers. 
@article{IM2_2013_77_4_a4,
     author = {Yu. G. Zarhin},
     title = {One-dimensional polynomial maps, periodic points and multipliers},
     journal = {Izvestiya. Mathematics},
     pages = {700--713},
     year = {2013},
     volume = {77},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2013_77_4_a4/}
}
TY  - JOUR
AU  - Yu. G. Zarhin
TI  - One-dimensional polynomial maps, periodic points and multipliers
JO  - Izvestiya. Mathematics
PY  - 2013
SP  - 700
EP  - 713
VL  - 77
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/IM2_2013_77_4_a4/
LA  - en
ID  - IM2_2013_77_4_a4
ER  - 
%0 Journal Article
%A Yu. G. Zarhin
%T One-dimensional polynomial maps, periodic points and multipliers
%J Izvestiya. Mathematics
%D 2013
%P 700-713
%V 77
%N 4
%U http://geodesic.mathdoc.fr/item/IM2_2013_77_4_a4/
%G en
%F IM2_2013_77_4_a4
Yu. G. Zarhin. One-dimensional polynomial maps, periodic points and multipliers. Izvestiya. Mathematics, Tome 77 (2013) no. 4, pp. 700-713. http://geodesic.mathdoc.fr/item/IM2_2013_77_4_a4/

[1] J.-P. Serre, Lie algebras and Lie groups, Lecture Notes in Math., 1500, Springer-Verlag, Berlin, 1992 | DOI | MR | Zbl

[2] Yu. G. Zarhin, “Polynomials in one variable and ranks of certain tangent maps”, Math. Notes, 91:4 (2012), 508–516 | DOI | DOI

[3] E. Rees, On a paper by Y. G. Zarhin, arXiv: abs/1105.4156

[4] G. T. Buzzard, S. L. Hruska, Yu. Ilyashenko, “Kupka–Smale theorem for polynomial automorphisms of $\mathbb C^2$ and persistence of heteroclinic intersections”, Invent. Math., 161:1 (2005), 45–89 | DOI | MR | Zbl

[5] I. Gorbovitskii, Netipichnost gomoklinicheskikh kasanii dlya polinomialnykh avtomorfizmov $\mathbb C^2$, sokhranyayuschikh ob'em, Diplomnaya rabota, MGU, 2006

[6] I. R. Shafarevich, Basic algebraic geometry, v. I, Springer-Verlag, New York–Heidelberg, 1994 | MR | MR | Zbl | Zbl

[7] J. S. Milne, Algebraic geometry, http://www.jmilne.org/math/CourseNotes/ag.html

[8] Y. Yomdin, “Singularities in algebraic data acquisition”, Real and complex singularities (Sao Carlos, Brazil, 2008), London Math. Soc. Lecture Note Ser., 380, Cambridge Univ. Press, Cambridge, 2010, 378–396 | MR | Zbl

[9] I. G. Macdonald, Symmetric functions and Hall polynomials, Clarendon Press, Oxford, 1979 | MR | Zbl

[10] J. Milnor, “Geometry and dynamics of quadratic rational maps”, Experiment. Math., 2:1 (1993), 37–83 | DOI | MR | Zbl