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Dynamical Systems: An Introduction undertakes the difficult task to provide a self-contained and compact introduction. Topics covered include topological, low-dimensional, hyperbolic and symbolic dynamics, as well as a brief introduction to ergodic theory. In particular, the authors consider topological recurrence, topological entropy, homeomorphisms and diffeomorphisms of the circle, Sharkovski's ordering, the Poincaré-Bendixson theory, and the construction of stable manifolds, as well as an introduction to geodesic flows and the study of hyperbolicity (the latter is often absent in a first introduction). Moreover, the authors introduce the basics of symbolic dynamics, the construction of symbolic codings, invariant measures, Poincaré's recurrence theorem and Birkhoff's ergodic theorem. The exposition is mathematically rigorous, concise and direct: all statements (except for some results from other areas) are proven. At the same time, the text illustrates the theory with many examples and 140 exercises of variable levels of difficulty. The only prerequisites are a background in linear algebra, analysis and elementary topology. This is a textbook primarily designed for a one-semester or two-semesters course at the advanced undergraduate or beginning graduate levels. It can also be used for self-study and as a starting point for more advanced topics. 410 0$aUniversitext,$x0172-5939 606 $aDynamics 606 $aErgodic theory 606 $aGlobal analysis (Mathematics) 606 $aManifolds (Mathematics) 606 $aDifferential equations 606 $aHyperbolic geometry 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aGlobal Analysis and Analysis on Manifolds$3https://scigraph.springernature.com/ontologies/product-market-codes/M12082 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aHyperbolic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21030 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aGlobal analysis (Mathematics). 615 0$aManifolds (Mathematics). 615 0$aDifferential equations. 615 0$aHyperbolic geometry. 615 14$aDynamical Systems and Ergodic Theory. 615 24$aGlobal Analysis and Analysis on Manifolds. 615 24$aOrdinary Differential Equations. 615 24$aHyperbolic Geometry. 676 $a515.352 700 $aBarreira$b Luis$4aut$4http://id.loc.gov/vocabulary/relators/aut$0472518 702 $aValls$b Claudia$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438158003321 996 $aDynamical Systems$92516817 997 $aUNINA