Comparison of dynamical degrees for semi-conjugate meromorphic maps

TL;DR

This paper derives formulas connecting the dynamical degrees of a meromorphic map, its relative map over a fibration, and the induced map on the base manifold, with applications to complex dynamics.

Contribution

It establishes new formulas relating dynamical degrees of meromorphic maps, their relative maps, and induced maps on fibrations, advancing understanding in complex dynamics.

Findings

Formulas relating dynamical degrees of f, f relative, and g.

Applications demonstrating the use of these formulas.

Insights into the behavior of meromorphic maps on fibrations.

Abstract

Let f be a dominant meromorphic self-map on a projective manifold X which preserves a meromorphic fibration pi: X --> Y of X over a projective manifold Y. We establish formulas relating the dynamical degrees of f, the dynamical degrees of f relative to the fibration and the dynamical degrees of the self-map g on Y induced by f. Applications are given.