Degree growth of birational maps of the plane

By J. Blanc, Julie D'eserti. 2011

50 citations recorded by the source corpus.

This article studies the sequence of iterative degrees of a birational map of the plane. This sequence is known either to be bounded or to have a linear, quadratic or exponential growth. The classification elements of infinite order with a bounded sequence of degrees is achieved, the case of elements of finite order being already known. The coefficients of the linear and quadratic growth are then described, and related to geometrical properties of the map. The dynamical number of base-points is also studied. Applications of our results are the description of embeddings of the Baumslag-Solitar groups and GL(2,Q) into the Cremona group.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2877699f851d3c3c2e1eee04af2ba56c39eee23e

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In Geometry and Topology

1. J. Blanc
2. Serge Cantat

Citations in the corpus

• Dynamical degrees of birational transformations of projective surfaces (2013, background): “An element f of the Cremona group is virtually isotopic to the identity if and only if f has finite order or f is conjugate to an element of Aut(P(2)k) = PGL3(k) (see [9]).”