Displaying similar documents to “Rational periodic points for quadratic maps”

The Nash problem of arcs and the rational double points D n

Camille Plénat (2008)

Annales de l’institut Fourier

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This paper deals with the Nash problem, which consists in comparing the number of families of arcs on a singular germ of surface U with the number of essential components of the exceptional divisor in the minimal resolution of this singularity. We prove their equality in the case of the rational double points D n ( n ≥ 4 ).

A generalization of Scholz’s reciprocity law

Mark Budden, Jeremiah Eisenmenger, Jonathan Kish (2007)

Journal de Théorie des Nombres de Bordeaux

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We provide a generalization of Scholz’s reciprocity law using the subfields K 2 t - 1 and K 2 t of ℚ ( ζ p ) , of degrees 2 t - 1 and 2 t over ℚ , respectively. The proof requires a particular choice of primitive element for K 2 t over K 2 t - 1 and is based upon the splitting of the cyclotomic polynomial Φ p ( x ) over the subfields.

Diagonal series of rational functions (several variables)

Sławomir Cynk, Piotr Tworzewski (1994)

Annales Polonici Mathematici

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We give representations of Nash functions in a neighbourhood of a polydisc (torus) in ℂ m as diagonal series of rational functions in a neighbourhood of a polydisc (torus) in ℂ m + 1 .

Infinite periodic points of endomorphisms over special confluent rewriting systems

Julien Cassaigne, Pedro V. Silva (2009)

Annales de l’institut Fourier

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We consider endomorphisms of a monoid defined by a special confluent rewriting system that admit a continuous extension to the completion given by reduced infinite words, and study from a dynamical viewpoint the nature of their infinite periodic points. For prefix-convergent endomorphisms and expanding endomorphisms, we determine the structure of the set of all infinite periodic points in terms of adherence values, bound the periods and show that all regular periodic points are attractors. ...

The higher transvectants are redundant

Abdelmalek Abdesselam, Jaydeep Chipalkatti (2009)

Annales de l’institut Fourier

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Let A , B denote generic binary forms, and let 𝔲 r = ( A , B ) r denote their r -th transvectant in the sense of classical invariant theory. In this paper we classify all the quadratic syzygies between the { 𝔲 r } . As a consequence, we show that each of the higher transvectants { 𝔲 r : r ≥ 2 } is redundant in the sense that it can be completely recovered from 𝔲 0 and 𝔲 1 . This result can be geometrically interpreted in terms of the incomplete Segre imbedding. The calculations rely upon the Cauchy exact sequence of S L 2 -representations,...

Equidistribution of Small Points, Rational Dynamics, and Potential Theory

Matthew H. Baker, Robert Rumely (2006)

Annales de l’institut Fourier

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Given a rational function ϕ ( T ) on ℙ 1 of degree at least 2 with coefficients in a number field k , we show that for each place v of k , there is a unique probability measure μ ϕ , v on the Berkovich space ℙ Berk , v 1 / ℂ v such that if { z n } is a sequence of points in ℙ 1 ( k ¯ ) whose ϕ -canonical heights tend to zero, then the z n ’s and their Gal ( k ¯ / k ) -conjugates are equidistributed with respect to μ ϕ , v . The proof uses a polynomial lift F ( x , y ) = ( F 1 ( x , y ) , F 2 ( x , y ) ) of ϕ to construct a two-variable Arakelov-Green’s function g ϕ , v ( x , y ) for each v . The measure μ ϕ , v is...