00965nam2 22002653i 450 SUN010114520150312105630.5420.0020150310d1926 |0itac50 baitaIT|||| |||||ˆ2:<<La ‰proprietà>>1.Pietro BonfanteRoma : Sampaolesi1926XIV453 p. ; 25 cmBiblioteca Lauria.001SUN01007422001 ˆ2: La ‰proprietàPietro Bonfante2.1210 RomaSampaolesi215 volumi25 cm.RomaSUNL000360Bonfante, Pietro1864-1932SUNV005835108947SampaolesiSUNV009590650ITSOL20190211RICASUN0101145UFFICIO DI BIBLIOTECA DEL DIPARTIMENTO DI GIURISPRUDENZA00CONS BL.900M.140 (2.1) 00BL 1944 20150310 Proprietà11433363UNICAMPANIA00954nam--2200349---450-99000607867020331620150928122238.0000607867USA01000607867(ALEPH)000607867USA0100060786720150928d1978----km-y0itay50------baitaIT||||||||001yyPortus LatisanaeCarlo Guido MorUdineSocietà Filologica Friulana1978112-120 p.22 cmEstratto da: Tisana, n. unico20012001LatisanaSec. 10.-13.BNCF945.3913303MOR,Carlo Guido154228ITsalbcISBD990006078670203316FC.OE. 11911330 FCilFC.OE.00346834BKFCILGENEROSO9020150928USA011222Portus Latisanae1514212UNISA04462nam 22005653u 450 991096744660332120250905102455.01-283-64388-X0-19-163752-1(CKB)2670000000269029(EBL)1043133(OCoLC)812197926(MiAaPQ)EBC1043133(OCoLC)792747080(FINmELB)ELB167386(EXLCZ)99267000000026902920130418d2012|||| u|| |engur|n|---|||||txtrdacontentcrdamediacrrdacarrierChaos and Fractals An Elementary Introduction1st ed.Oxford OUP Oxford20121 online resource (431 p.)Description based upon print version of record.0-19-956644-5 Includes bibliographical references and index.Cover; Contents; I: Introducing Discrete Dynamical Systems; 0 Opening Remarks; 0.1 Chaos; 0.2 Fractals; 0.3 The Character of Chaos and Fractals; 1 Functions; 1.1 Functions as Actions; 1.2 Functions as a Formula; 1.3 Functions are Deterministic; 1.4 Functions as Graphs; 1.5 Functions as Maps; Exercises; 2 Iterating Functions; 2.1 The Idea of Iteration; 2.2 Some Vocabulary and Notation; 2.3 Iterated Function Notation; 2.4 Algebraic Expressions for Iterated Functions; 2.5 Why Iteration?; Exercises; 3 Qualitative Dynamics: The Fate of the Orbit; 3.1 Dynamical Systems3.2 Dynamics of the Squaring Function3.3 The Phase Line; 3.4 Fixed Points via Algebra; 3.5 Fixed Points Graphically; 3.6 Types of Fixed Points; Exercises; 4 Time Series Plots; 4.1 Examples of Time Series Plots; Exercises; 5 Graphical Iteration; 5.1 An Initial Example; 5.2 The Method of Graphical Iteration; 5.3 Further Examples; Exercises; 6 Iterating Linear Functions; 6.1 A Series of Examples; 6.2 Slopes of +1 or -1; Exercises; 7 Population Models; 7.1 Exponential Growth; 7.2 Modifying the Exponential Growth Model; 7.3 The Logistic Equation; 7.4 A Note on the Importance of Stability7.5 Other r ValuesExercises; 8 Newton, Laplace, and Determinism; 8.1 Newton and Universal Mechanics; 8.2 The Enlightenment and Optimism; 8.3 Causality and Laplace's Demon; 8.4 Science Today; 8.5 A Look Ahead; II: Chaos; 9 Chaos and the Logistic Equation; 9.1 Periodic Behavior; 9.2 Aperiodic Behavior; 9.3 Chaos Defined; 9.4 Implications of Aperiodic Behavior; Exercises; 10 The Butterfly Effect; 10.1 Stable Periodic Behavior; 10.2 Sensitive Dependence on Initial Conditions; 10.3 SDIC Defined; 10.4 Lyapunov Exponents; 10.5 Stretching and Folding: Ingredients for Chaos10.6 Chaotic Numerics: The Shadowing LemmaExercises; 11 The Bifurcation Diagram; 11.1 A Collection of Final-State Diagrams; 11.2 Periodic Windows; 11.3 Bifurcation Diagram Summary; Exercises; 12 Universality; 12.1 Bifurcation Diagrams for Other Functions; 12.2 Universality of Period Doubling; 12.3 Physical Consequences of Universality; 12.4 Renormalization and Universality; 12.5 How are Higher-Dimensional Phenomena Universal?; Exercises; 13 Statistical Stability of Chaos; 13.1 Histograms of Periodic Orbits; 13.2 Histograms of Chaotic Orbits; 13.3 Ergodicity; 13.4 Predictable Unpredictability16.6 Fractals, Defined AgainThis book provides the reader with an elementary introduction to chaos and fractals, suitable for students with a background in elementary algebra, without assuming prior coursework in calculus or physics. It introduces the key phenomena of chaos - aperiodicity, sensitive dependence on initial conditions, bifurcations - via simple iterated functions. Fractals are introduced as self-similar geometric objects and analyzed with the self-similarity and box-counting dimensions. After abrief discussion of power laws, subsequent chapters explore Julia Sets and the Mandelbrot Set. The last part of theChaotic behavior in systemsDifferentiable dynamical systemsFractalsChaotic behavior in systems.Differentiable dynamical systems.Fractals.515.39Feldman David P275401AU-PeELAU-PeELAU-PeELBOOK9910967446603321Chaos and fractals257830UNINA