Invariant curves for birational surface maps

DOI10.1090/S0002-9947-07-04162-1zbMath1115.14007arXivmath/0505014OpenAlexW1501936463MaRDI QIDQ3425966

Daniel Jackson, Jeffrey Diller, Andrew John Sommese

Publication date: 7 March 2007

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0505014

zbMATH Keywords

complex dynamicsbirational mapinvariant curve

Mathematics Subject Classification ID

Birational automorphisms, Cremona group and generalizations (14E07) Special algebraic curves and curves of low genus (14H45) Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables (32H50)

Related Items (17)

Rational surface automorphisms preserving cuspidal anticanonical curves ⋮ Algebraic webs invariant under endomorphisms ⋮ Rational surface maps with invariant meromorphic two-forms ⋮ Automorphisms of surfaces: Kummer rigidity and measure of maximal entropy ⋮ Siegel disks on rational surfaces ⋮ Finite orbits for large groups of automorphisms of projective surfaces ⋮ An automorphism group of a rational surface: not too big not too small ⋮ Embeddings of \(\mathrm{SL}(2, \mathbb Z)\) into the Cremona group ⋮ Infinitesimal deformations of rational surface automorphisms ⋮ On the complex dynamics of birational surface maps defined over number fields ⋮ Dynamics of rational surface automorphisms: linear fractional recurrences ⋮ Cremona transformations, surface automorphisms, and plain cubics. With an appendix by Igor Dolgachev ⋮ Periodic points for area-preserving birational maps of surfaces ⋮ On birational transformations of pairs in the complex plane ⋮ Commensurating actions of birational groups and groups of pseudo-automorphisms ⋮ Entropy of Real Rational Surface Automorphisms ⋮ Periodic points of birational transformations on projective surfaces

Cites Work

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• Complex Hénon mappings in \({\mathbb{C}}^ 2\) and Fatou-Bieberbach domains
• Points périodiques d'applications birationnelles de \({\mathbb P}^2\). (Periodic points for birational mappings of \({\mathbb P}^2\).)
• Linearity of the exceptional set for maps of \(\mathbf P_k(\mathbb{C})\)
• Energy and invariant measures for birational surface maps
• Dynamics of a two parameter family of plane birational maps: maximal entropy
• Dynamics of bimeromorphic maps of surfaces
• Real and complex dynamics of a family of birational maps of the plane: The golden mean subshift

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