| We discuss various algebraic, geometric and dynamical properties of the holomorphic self-maps of complex projective manifolds.;Self-maps of P2 with invariant elliptic curves. If a regular self-map of P2 leaves invariant an elliptic plane curve C, the closure of the backward orbit of any point on C equals the Julia set. For smooth cubics, two types of self-maps are discussed: tangent processes, and elementary maps. For singular elliptic curves, invariants are defined at the singular points, and calculated for several families of curves: duals of smooth cubics, and elliptic quartics with two singular points.;Self-maps of ruled surfaces. We give a systematic description of the self-maps of ruled surfaces. The discussion is based on the rigidity of the curves with negative or zero self-intersection. The configurations of completely invariant curves is listed, and an application to the dynamics of elementary maps of P2 is deduced.;Completely invariant hypersurfaces in projective spaces. We discuss the structure of those hypersurfaces that are completely invariant for some rational self-map of Pn . This involves the study of essential hypersurfaces, Bottcher divisors, degenerate essential components and stars.;Self-maps of projective bundles. Given a self-map of a projective bundle over Pn , we study its geometry (fiber-degree, algebraic degree, lifting to the dual vector bundle) and its dynamics (Green function, Fatou components, Julia set). |
