The Dynamical Degrees of a Mapping

Abstract

Let f be a rational mapping of a space X . The complexity of (f,X) as a dynamical system is measured by the dynamical degrees ${\delta }_p(f)$, $1\le p\le \dim (X)$. We give the definition of the dynamical degrees show how they are computed in certain cases. For instance, we show that if the dynamical degree of an automorphism of a Kähler manifold is greater than one, then it must be irrational.

References in corpus (2)

• Pulling Back Cohomology Classes and Dynamical Degrees Of Monomial Maps
• Degree complexity of birational maps related to matrix inversion: Symmetric case

Cited by in corpus (8)

• On automorphisms of blowups of ${\mathbb{P}}^3$
• On automorphisms of blowups of projective manifolds
• Computing dynamical degrees
• Hurwitz correspondences on compactifications of ${\mathcal{M}}_{0,N}$
• Zero Entropy for Some Birational Maps of C^2
• Dynamical Classification of a Family of Birational Maps of C^2 via Algebraic Entropy
• Invertible dynamics on blow-ups of P^k
• Degree Growth of Rational Maps Induced from Algebraic Structures