LEADER 04377nam 22007455 450 001 996466543003316 005 20200703045902.0 010 $a3-319-72179-8 024 7 $a10.1007/978-3-319-72179-8 035 $a(CKB)4100000002485383 035 $a(DE-He213)978-3-319-72179-8 035 $a(MiAaPQ)EBC6295627 035 $a(MiAaPQ)EBC5592281 035 $a(Au-PeEL)EBL5592281 035 $a(OCoLC)1066185896 035 $a(PPN)224637673 035 $a(EXLCZ)994100000002485383 100 $a20180206d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aOpen Conformal Systems and Perturbations of Transfer Operators$b[electronic resource] /$fby Mark Pollicott, Mariusz Urba?ski 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XII, 204 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2206 311 $a3-319-72178-X 320 $aIncludes bibliographical references and index. 327 $a1. Introduction -- 2. Singular Perturbations of Classical Original Perron?Frobenius Operators on Countable Alphabet Symbol Spaces -- 3. Symbol Escape Rates and the Survivor Set K(Un) -- 4. Escape Rates for Conformal GDMSs and IFSs -- 5. Applications: Escape Rates for Multimodal Maps and One-Dimensional Complex Dynamics. 330 $aThe focus of this book is on open conformal dynamical systems corresponding to the escape of a point through an open Euclidean ball. The ultimate goal is to understand the asymptotic behavior of the escape rate as the radius of the ball tends to zero. In the case of hyperbolic conformal systems this has been addressed by various authors. The conformal maps considered in this book are far more general, and the analysis correspondingly more involved. The asymptotic existence of escape rates is proved and they are calculated in the context of (finite or infinite) countable alphabets, uniformly contracting conformal graph-directed Markov systems, and in particular, conformal countable alphabet iterated function systems. These results have direct applications to interval maps, meromorphic maps and rational functions. Towards this goal the authors develop, on a purely symbolic level, a theory of singular perturbations of Perron--Frobenius (transfer) operators associated with countable alphabet subshifts of finite type and Hölder continuous summable potentials. This leads to a fairly full account of the structure of the corresponding open dynamical systems and their associated surviving sets. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2206 606 $aDynamics 606 $aErgodic theory 606 $aFunctional analysis 606 $aFunctions of complex variables 606 $aOperator theory 606 $aMeasure theory 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aFunctions of a Complex Variable$3https://scigraph.springernature.com/ontologies/product-market-codes/M12074 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 606 $aMeasure and Integration$3https://scigraph.springernature.com/ontologies/product-market-codes/M12120 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aFunctional analysis. 615 0$aFunctions of complex variables. 615 0$aOperator theory. 615 0$aMeasure theory. 615 14$aDynamical Systems and Ergodic Theory. 615 24$aFunctional Analysis. 615 24$aFunctions of a Complex Variable. 615 24$aOperator Theory. 615 24$aMeasure and Integration. 676 $a516.35 700 $aPollicott$b Mark$4aut$4http://id.loc.gov/vocabulary/relators/aut$060528 702 $aUrba?ski$b Mariusz$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466543003316 996 $aOpen conformal systems and perturbations of transfer operators$91749800 997 $aUNISA