LEADER 04069nam 22006135 450 001 9910300098603321 005 20200705045621.0 010 $a3-319-90110-9 024 7 $a10.1007/978-3-319-90110-7 035 $a(CKB)4100000004243949 035 $a(DE-He213)978-3-319-90110-7 035 $a(MiAaPQ)EBC5379791 035 $a(PPN)227404327 035 $a(EXLCZ)994100000004243949 100 $a20180502d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAdmissibility and Hyperbolicity /$fby Luís Barreira, Davor Dragi?evi?, Claudia Valls 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (IX, 145 p.) 225 1 $aSpringerBriefs in Mathematics,$x2191-8198 311 $a3-319-90109-5 327 $a1. Introduction -- 2. Exponential Contractions -- 3. Exponential Dichotomies: Discrete Time -- 4. Exponential Dichotomies: Continuous Time -- 5. Admissibility: Further Developments -- 6. Applications of Admissibility -- References -- Index. 330 $aThis book gives a comprehensive overview of the relationship between admissibility and hyperbolicity. Essential theories and selected developments are discussed with highlights to applications. The dedicated readership includes researchers and graduate students specializing in differential equations and dynamical systems (with emphasis on hyperbolicity) who wish to have a broad view of the topic and working knowledge of its techniques. The book may also be used as a basis for appropriate graduate courses on hyperbolicity; the pointers and references given to further research will be particularly useful. The material is divided into three parts: the core of the theory, recent developments, and applications. The first part pragmatically covers the relation between admissibility and hyperbolicity, starting with the simpler case of exponential contractions. It also considers exponential dichotomies, both for discrete and continuous time, and establishes corresponding results building on the arguments for exponential contractions. The second part considers various extensions of the former results, including a general approach to the construction of admissible spaces and the study of nonuniform exponential behavior. Applications of the theory to the robustness of an exponential dichotomy, the characterization of hyperbolic sets in terms of admissibility, the relation between shadowing and structural stability, and the characterization of hyperbolicity in terms of Lyapunov sequences are given in the final part. . 410 0$aSpringerBriefs in Mathematics,$x2191-8198 606 $aDynamics 606 $aErgodic theory 606 $aDifferential equations 606 $aDifference equations 606 $aFunctional equations 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aDifference and Functional Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12031 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aDifferential equations. 615 0$aDifference equations. 615 0$aFunctional equations. 615 14$aDynamical Systems and Ergodic Theory. 615 24$aOrdinary Differential Equations. 615 24$aDifference and Functional Equations. 676 $a515.39 676 $a515.48 700 $aBarreira$b Luís$4aut$4http://id.loc.gov/vocabulary/relators/aut$0472518 702 $aDragi?evi?$b Davor$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aValls$b Claudia$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910300098603321 996 $aAdmissibility and Hyperbolicity$92102298 997 $aUNINA