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Holomorphic Dynamical Systems pp 57–104Cite as

Dynamics of Rational Surface Automorphisms

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Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 1998))

Abstract

This is a 2-part introduction to the dynamics of rational surface automorphisms. Such maps can be written in coordinates as rational functions or polynomials. The first part concerns polynomial automorphisms of complex 2-space and includes the complex Henon family.

The second part concerns compact (complex) rational surfaces. The basic properties of automorphisms of positive entropy are given, as well as the construction of invariant currents and measures. This is illustrated by a number of examples.

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Authors and Affiliations

  1. Department of Mathematics, Indiana University, 47405, Bloomington, IN, USA

    Eric Bedford

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  1. Eric Bedford
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Correspondence to Eric Bedford .

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Editors and Affiliations

  1. Department of Mathematics "U.Dini", University of Florence, viale Morgagni 67/A, Firenze, 50134, Italy

    Graziano Gentili

  2. Dipartimento di Strutture, Università della Calabria, Ponte Pietro Bucci 39, Arcavacata di Rende (CS), 87036, Italy

    Jacques Guenot

  3. Dipartimento di Matematica "U.Dini", Università di Firenze, viale Morgagni 67/A, Firenze, 50134, Italy

    Giorgio Patrizio

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Bedford, E. (2010). Dynamics of Rational Surface Automorphisms. In: Gentili, G., Guenot, J., Patrizio, G. (eds) Holomorphic Dynamical Systems. Lecture Notes in Mathematics(), vol 1998. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13171-4_2

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