#DILLER GOLDEN MEAN SUBSHIFT BEDFORD HOW TO#
I will show how to prove existence and non-existence of H-polar cylinders This notion links together affine, birational and Kähler geometries. Ivan CHELTSOV - Cylinders in del Pezzo surfacesįor a projective variety X and an ample divisor H on it, an H-polar cylinder in X is an open ruled affine subset whose complement is a support of an effective -divisor -rationally equivalent to H. Determining this order is interesting and difficult, possibly even equivalent to the deformation problem for plane curve singularities. These are partially ordered by inclusion. Links associated with plane curve singularities come with a natural fibre surface in the 3-sphere. Talks - titles and abstracts Sebastian BAADER - A partial order on plane curve singularities Rational surface maps with invariant meromorphic two forms. Jeffrey Diller, Romain Dujardin, and Vincent Guedj.ĭynamics of meromorphic maps with small topological degree I: from cohomology to currents. Cremona transformations, surface automorphisms, and plane cubics. Dynamics of bimeromorphic maps of surfaces. Real and complex dynamics of a family of birational maps of the plane: the golden mean subshift. On dynamics of birational maps, perhaps including results about non-invertible rational maps, maps with invariant two forms, or the construction of automorphisms on blowups of the projective plane.Įric Bedford and Jeffrey Diller. To deal with more general birational maps, I will introduce the notions of Green current, laminarity and geometric intersection of positive closed currents.Īny remaining time will be devoted to surveying more recent work A particular example studied by Bedford and myself will serve as useful Leads to an understanding of the ergodic theory of the map. Next I will describe the way in which cohomological informationĮncapsulated by the pullback action induced by a birational self-map I will then describe the dynamical classication of birational surface maps by "degree growth" presented in the article by Favre and myself. Surfaces, I will describe the important notions of algebraic stability and first dynamical degree. My main goal will be to describe how the dynamics of such a map is determined by the linear pullback action it induces on the Picard group of an appropriately chosen rational surface.īeginning with some generalities about rational maps and rational
#DILLER GOLDEN MEAN SUBSHIFT BEDFORD SERIES#
In this series of introductory lectures I will survey work done toward understanding dynamics of plane birational maps. Jeffrey DILLER - Birational maps and dynamics on rational surfaces Kim, Pseudoautomorphisms with invariant elliptic curves, arXiv:1401.2386 Perroni and D-Q Zhang, Pseudo-automorphisms of positive entropy on the blowups of products of projective spaces. Kim, Dynamics of (pseudo) automorphisms of 3-space: periodicity versus positive entropy. Proceedings of the Workshop Future Directions in Difference Equations, 3-13, Colecc. Bedford, The dynamical degrees of a mapping. Smillie, Polynomial diffeomorphisms of 2. Smillie, Polynomial diffeomorphisms of 2: currents, equilibrium measure and hyperbolicity. Bedford, Invertible dynamics on blow-ups of k, arXiv:1411.0760Į. Iteration, these behave almost as well as automorphisms, but the indeterminacy locus can cause problems. These are birational maps f for which neither f nor f -1 has an exceptional hypersurface. Discussion of pseudo-automorphisms in dimension 3 (and higher) (see ). The most basic of these is the first dynamical degree δ 1, but we will discuss the others, too.ģ. In (complex) dimension k, thereĪre dynamical degrees δ ℓ in all codimensions 1≤ℓ≤ k. TheseĪre perhaps the most invariants of birational conjugacy.
A rather general discussion of dynamical degrees of rational maps (see ). This is intended to give a background which will illuminate the difficulties which arise in theĢ.
Some methods that have been applied successfully to the case of biregular maps. The purpose of this lecture(s) is to present the questions and The Hénon family consists of (holomorphic) polynomial diffeomorphisms of 2, which haveīirational extensions to 2. The dynamics of the Hénon family of automorphisms of 2 (see, ). Specifically, we plan to work with the following topics:ġ. In this series of lectures we intend to outline some aspects of the dynamical theory of birational maps (in dim 2 and higher) which are at least close to being automorphisms. Mini-courses - titles and abstracts Eric BEDFORD - Dynamics of Birational Maps
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