{"product_id":"haissinsky-peter-asterisque-ndeg-325-coarse-expanding-conformal-dynamics-9782856292662","title":"Astérisque, n° 325. Coarse expanding conformal dynamics","description":"\u003cp\u003eMotivated by the dynamics of rational maps, we introduce a class\n of topological dynamical systems satisfying certain topological regularity,\n expansion, irreducibility, and finiteness conditions. We\n call such maps \"topologically coarse expanding conformal\" (top.\n CXC) dynamical systems. Given such a system \u003ci\u003ef\u003c\/i\u003e : \u003ci\u003eX\u003c\/i\u003e Vecteur \u003ci\u003eX\u003c\/i\u003e and a\n finite cover of \u003ci\u003eX\u003c\/i\u003e by connected open sets, we construct a negatively\n curved infinite graph on which \u003ci\u003ef\u003c\/i\u003e acts naturally by local isometries.\n The induced topological dynamical system on the boundary at infinity\n is naturally conjugate to the dynamics of \u003ci\u003ef.\u003c\/i\u003e This implies that\n \u003ci\u003eX\u003c\/i\u003e inherits metrics in which the dynamics of \u003ci\u003ef\u003c\/i\u003e satisfies the Principle\n of the Conformal Elevator: arbitrarily small balls may be blown\n up with bounded distortion to nearly round sets of definite size.\n This property is preserved under conjugation by a quasisymmetric\n map, and top. CXC dynamical systems on a metric space satisfying\n this property we call \"metrically CXC\". The ensuing results deepen\n the analogy between rational maps and Kleinian groups by extending\n it to analogies between metric CXC systems and hyperbolic\n groups. We give many examples and several applications. In particular,\n we provide a new interpretation of the characterization of\n rational functions among topological maps and of generalized Lattès\n examples among uniformly quasiregular maps. \u003ci\u003eVia\u003c\/i\u003e techniques\n in the spirit of those used to construct quasiconformal measures for\n hyperbolic groups, we also establish existence, uniqueness, naturality,\n and metric regularity properties for the measure of maximal\n entropy of such systems.\u003c\/p\u003e","brand":"Amer Mathematical Society","offers":[{"title":"Default Title","offer_id":53813690925398,"sku":null,"price":0.0,"currency_code":"EUR","in_stock":false}],"url":"https:\/\/www.momoxbooks.com\/products\/haissinsky-peter-asterisque-ndeg-325-coarse-expanding-conformal-dynamics-9782856292662","provider":"momoxbooks","version":"1.0","type":"link"}