By Curtis T. McMullen
Many parallels among complicated dynamics and hyperbolic geometry have emerged long ago decade. construction on paintings of Sullivan and Thurston, this booklet offers a unified remedy of the development of fixed-points for renormalization and the development of hyperbolic three- manifolds fibering over the circle.
Both matters are studied through geometric limits and pressure. This strategy exhibits open hyperbolic manifolds are rigid, and yields quantitative opposite numbers to Mostow pressure. In complicated dynamics, it motivates the development of towers of quadratic-like maps, and results in a quantitative evidence of convergence of renormalization.
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