Periodic points of birational maps on projective surfaces

Abstract

We classify birational maps of projective smooth surfaces whose non-critical periodic points are Zariski dense. In particular, we show that if the first dynamical degree is greater than one, then the periodic points are Zariski dense.

30 pages

References in corpus (3)

• Questions on self maps of algebraic varieties
• Normal subgroups in the Cremona group (long version)
• Transformations birationnelles de petit degré

Cited by in corpus (24)

• Relative dynamical degrees of correspondences over a field of arbitrary characteristic
• Dynamical degrees of birational transformations of projective surfaces
• (Relative) dynamical degrees of rational maps over an algebraic closed field
• The existence of Zariski dense orbits for polynomial endomorphisms of the affine plane
• Growth of the number of periodic points for meromorphic maps
• Stability and bifurcations for dissipative polynomial automorphisms of C^2
• Super-potentials, densities of currents and number of periodic points for holomorphic maps
• Dynamical Degrees, Arithmetic Degrees, and Canonical Heights for Dominant Rational Self-Maps of Projective Space
• On the Medvedev-Scanlon Conjecture for Minimal Threefolds of Non-Negative Kodaira Dimension
• The existence of Zariski dense orbits for endomorphisms of projective surfaces (with an appendix in collaboration with Thomas Tucker)
• Density of orbits of endomorphisms of commutative linear algebraic groups
• Relations between dynamical degrees, Weil's Riemann hypothesis and the standard conjectures
• Minimum positive entropy of complex Enriques surface automorphisms
• Finiteness properties of pseudo-hyperbolic varieties
• A theorem of Tits type for automorphism groups of projective varieties in arbitrary characteristic (with an appendix by Tomohide Terasoma)
• Free algebras arising from positive-entropy automorphisms of surfaces
• Degeneration of Dynamical Degrees in Families of Maps
• Three chapters on Cremona groups
• Some properties of dynamical degrees with a view towards cubic fourfolds
• Invertible dynamics on blow-ups of P^k
• Algebraic dynamics of skew-linear self-maps
• On endomorphisms of projective varieties with numerically trivial canonical divisors
• Some applications of p-adic uniformization to algebraic dynamics
• Salem numbers and Enriques surfaces