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The theory of holomorphic dynamical systems is a subject of increasing interest in mathematics, both for its challenging problems and for its connections with other branches of pure and applied mathematics. This volume collects the Lectures held at the 2008 CIME session on "Holomorphic Dynamical Systems" held in Cetraro, Italy. This CIME Course focused on a number of important topics in the study of discrete and continuous dynamical systems, including both local and global aspects, providing a fascinating introduction to many key problems in current research. The contributions provide an ample description of the phenomena occurring in central themes of holomorphic dynamics such as automorphisms and meromorphic self-maps of projective spaces, of entire maps on complex spaces and holomorphic foliations in surfaces and higher dimensional manifolds, elaborating on the different techniques used and familiarizing readers with the latest findings on current research topics.

Holomorphic functions --- Differentiable dynamical systems --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Mathematical Theory --- Functions, Holomorphic --- Mathematics. --- Dynamics. --- Ergodic theory. --- Functions of complex variables. --- Potential theory (Mathematics). --- Dynamical Systems and Ergodic Theory. --- Functions of a Complex Variable. --- Several Complex Variables and Analytic Spaces. --- Potential Theory. --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Complex variables --- Elliptic functions --- Functions of real variables --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Physics --- Statics --- Math --- Science --- Functions of several complex variables --- Differentiable dynamical systems. --- Differential equations, partial. --- Partial differential equations --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Cetraro <2008>