01048nam 2200373 450 991015024860332120170429092312.00-7660-8101-X(CKB)3710000000942212(MiAaPQ)EBC5533390(EXLCZ)99371000000094221220181016d2017 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierThis is my doctor /Adam BellamyNew York, NY :Enslow Publishing,2017.1 online resource (24 pages) illustrationsAll about my world0-7660-8100-1 Includes bibliographical references and index.PhysiciansJuvenile literaturePhysicians610.69/5Bellamy Adam1246098MiAaPQMiAaPQMiAaPQBOOK9910150248603321This is my doctor2896205UNINA03231nam 2200589 450 991079433550332120201204065151.01-4704-6245-1(CKB)4100000011437134(MiAaPQ)EBC6346625(RPAM)21679387(PPN)250910098(EXLCZ)99410000001143713420201204d2020 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierConformal graph directed Markov systems on Carnot groups /Vasilionis Chousionis, Jeremy Tyson, Mariusz UrbanskiProvidence, Rhode Island :American Mathematical Society,[2020]©20201 online resource (170 pages)Memoirs of the American Mathematical Society ;Volume 266"Forthcoming, volume 266, number 1291."1-4704-4215-9 Includes bibliographical references and index.Carnot 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."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"--Provided by publisher.Memoirs of the American Mathematical Society ;Number 266.ThermodynamicsMathematical modelsMarkov processesConformal mappingNilpotent Lie groupsHausdorff measuresThermodynamicsMathematical models.Markov processes.Conformal mapping.Nilpotent Lie groups.Hausdorff measures.621.402130L1053C1737C4011J7028A7837B1037C3037D3537F3547H10mscChousionis Vasilionis1980-1539880Urbański MariuszTyson Jeremy T.1972-MiAaPQMiAaPQMiAaPQBOOK9910794335503321Conformal graph directed Markov systems on Carnot groups3791056UNINA