85 research outputs found
On automorphisms of Enriques surfaces and their entropy
Consider an arbitrary automorphism of an Enriques surface with its lift to
the covering K3 surface. We prove a bound of the order of the lift acting on
the anti-invariant cohomology sublattice of the Enriques involution. We use it
to obtain some mod 2 constraint on the original automorphism. As an
application, we give a necessary condition for Salem numbers to be dynamical
degrees on Enriques surfaces and obtain a new lower bound on the minimal value.
In the Appendix, we give a complete list of Salem numbers that potentially may
be the minimal dynamical degree on Enriques surfaces and for which the
existence of geometric automorphisms is unknown.Comment: 16 pages / v2: some refinements on the theorems and the proofs, and
also attached plain text lists of Salem numbers related to the proble
On the stable dynamical spectrum of complex surfaces
We characterize Salem numbers which have some power arising as dynamical degree of an automorphism on a complex (projective) 2-Torus, K3 or Enriques surface
Dynamical degrees of birational transformations of projective surfaces
The dynamical degree of a birational transformation measures
the exponential growth rate of the degree of the formulae that define the
-th iterate of . We study the set of all dynamical degrees of all
birational transformations of projective surfaces, and the relationship between
the value of and the structure of the conjugacy class of . For
instance, the set of all dynamical degrees of birational transformations of the
complex projective plane is a closed and well ordered set of algebraic numbers.Comment: 65 page
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