LEADER 03231nam 2200589 450 001 9910812622103321 005 20201204065151.0 010 $a1-4704-6245-1 035 $a(CKB)4100000011437134 035 $a(MiAaPQ)EBC6346625 035 $a(RPAM)21679387 035 $a(PPN)250910098 035 $a(EXLCZ)994100000011437134 100 $a20201204d2020 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aConformal graph directed Markov systems on Carnot groups /$fVasilionis Chousionis, Jeremy Tyson, Mariusz Urbanski 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2020] 210 4$dİ2020 215 $a1 online resource (170 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vVolume 266 300 $a"Forthcoming, volume 266, number 1291." 311 $a1-4704-4215-9 320 $aIncludes bibliographical references and index. 327 $aCarnot groups -- Carnot groups of Iwasawa type and conformal mappings -- Metric and geometric properties of conformal maps -- Conformal graph directed Markov systems -- Examples of GDMS in Carnot groups -- Countable alphabet symbolic dynamics : foundations of the thermodynamic formalism -- Hausdorff dimension of limit sets -- Conformal measures and regularity of domains -- Examples revisited -- Finer properties of limit sets : Hausdorff, packing and invariant measures -- Equivalent separation conditions for finite GDMS. 330 $a"We develop a comprehensive theory of conformal graph directed Markov systems in the non-Riemannian setting of Carnot groups equipped with a sub-Riemannian metric. In particular, we develop the thermodynamic formalism and show that, under natural hypotheses, the limit set of an Carnot conformal GDMS has Hausdorff dimension given by Bowen's parameter. We illustrate our results for a variety of examples of both linear and nonlinear iterated function systems and graph directed Markov systems in such sub-Riemannian spaces. These include the Heisenberg continued fractions introduced by Lukyanenko and Vandehey as well as Kleinian and Schottky groups associated to the non-real classical rank one hyperbolic spaces"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society ;$vNumber 266. 606 $aThermodynamics$xMathematical models 606 $aMarkov processes 606 $aConformal mapping 606 $aNilpotent Lie groups 606 $aHausdorff measures 615 0$aThermodynamics$xMathematical models. 615 0$aMarkov processes. 615 0$aConformal mapping. 615 0$aNilpotent Lie groups. 615 0$aHausdorff measures. 676 $a621.4021 686 $a30L10$a53C17$a37C40$a11J70$a28A78$a37B10$a37C30$a37D35$a37F35$a47H10$2msc 700 $aChousionis$b Vasilionis$f1980-$01722265 702 $aUrban?ski$b Mariusz 702 $aTyson$b Jeremy T.$f1972- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910812622103321 996 $aConformal graph directed Markov systems on Carnot groups$94122485 997 $aUNINA