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John Milnor, best known for his work in differential topology, K-theory, and dynamical systems, is one of only three mathematicians to have won the Fields medal, the Abel prize, and the Wolf prize, and is the only one to have received all three of the Leroy P. Steele prizes. In honor of his eightieth birthday, this book gathers together surveys and papers inspired by Milnor's work, from distinguished experts examining not only holomorphic dynamics in one and several variables, but also differential geometry, entropy theory, and combinatorial group theory. The book contains the last paper written by William Thurston, as well as a short paper by John Milnor himself. Introductory sections put the papers in mathematical and historical perspective, color figures are included, and an index facilitates browsing. This collection will be useful to students and researchers for decades to come. The contributors are Marco Abate, Marco Arizzi, Alexander Blokh, Thierry Bousch, Xavier Buff, Serge Cantat, Tao Chen, Robert Devaney, Alexandre Dezotti, Tien-Cuong Dinh, Romain Dujardin, Hugo García-Compeán, William Goldman, Rotislav Grigorchuk, John Hubbard, Yunping Jiang, Linda Keen, Jan Kiwi, Genadi Levin, Daniel Meyer, John Milnor, Carlos Moreira, Vincente Muñoz, Viet-Anh Nguyên, Lex Oversteegen, Ricardo Pérez-Marco, Ross Ptacek, Jasmin Raissy, Pascale Roesch, Roberto Santos-Silva, Dierk Schleicher, Nessim Sibony, Daniel Smania, Tan Lei, William Thurston, Vladlen Timorin, Sebastian van Strien, and Alberto Verjovsky.

Functions of complex variables. --- Differentiable dynamical systems. --- Milnor, John W. --- John Milnor. --- Jordan curves. --- Julia sets. --- K-theory. --- M. Hakim. --- Maldelbrot set. --- Milnor's conjecture. --- Sierpinski carpets. --- Sierpinski gaskets. --- Thurston Rigidity Theorem. --- William Thurston. --- antiholomorphic quadratic polynomials. --- antiholomorphic unicritical polynomials. --- arithmetics. --- asymptotic behavior. --- automorphisms. --- biholomorphisms. --- combinatorial group theory. --- complex manifolds. --- complex polynomials. --- conformal distortion. --- conjugacy. --- connectedness loci. --- critical objects. --- critical point. --- critically finite case. --- decomposition. --- differential geometry. --- differential topology. --- dynamical cores. --- dynamical derivatives. --- dynamical scales. --- dynamical systems. --- dynamics. --- eigenvalues. --- entropy theory. --- entropy. --- escape regions. --- expanding critical orbits. --- external rays. --- geometrically finite rational maps. --- global meromorphic maps. --- holomorphic dynamics studies. --- holomorphic dynamics. --- holomorphic germs. --- holomorphic maps. --- hyperbolic distortion. --- hyperbolic geometry. --- hyperbolicity. --- identity germ. --- implosions. --- index theorems. --- infinitely renormalizable quadratic polynomials. --- integral closure. --- interval dynamics. --- irreducibility. --- kneading sequences. --- laminations. --- leading monomial vector. --- leading monomials. --- limiting behavior. --- local connectivity. --- local dynamics. --- mathematics. --- mating. --- metric stability. --- monotonicity. --- multicorn. --- non-locally connected Julia sets. --- one-dimensional maps. --- periodic critical orbit. --- periodic objects. --- periodic orbits. --- perturbations. --- polynomials. --- postcritically finite maps. --- projective space. --- pushforwards. --- quadratic differentials. --- quadratic dynatomic curves. --- quadratic polynomials. --- random walks. --- rational maps. --- renormalization theory. --- resurgence theory. --- rigidity. --- robustness. --- singularly perturbed rational maps. --- smoothness. --- spherical geometry. --- summability condition. --- summable critical points. --- topological entropy. --- topological polynomials. --- topological space. --- transversality theory. --- tricorn. --- unbounded hyperbolic components. --- unicritical polynomial maps. --- unimodal interval map. --- unmating.