03653nam 2200613 450 991082915050332120230120014648.01-4832-6908-6(CKB)3710000000200396(EBL)1901513(SSID)ssj0001266574(PQKBManifestationID)12564617(PQKBTitleCode)TC0001266574(PQKBWorkID)11249538(PQKB)10838653(MiAaPQ)EBC1901513(EXLCZ)99371000000020039620150202h19861986 uy 0engur|n|---|||||txtccrChaotic dynamics and fractals /edited by Michael F. Barnsley, Stephen G. DemkoOrlando, Florida ;London, England :Academic Press, Inc.,1986.©19861 online resource (305 p.)Notes and Reports in Mathematics in Science and Engineering ;Volume 2Description based upon print version of record.1-322-55828-0 0-12-079060-2 Includes bibliographical references at the end of each chapters.Front Cover; Chaotic Dynamics and Fractals; Copyright Page; Table of Contents; Contributors; Preface; Part I: Chaos and Fractals; CHAPTER 1. CHAOS: SOLVING THE UNSOLVABLE, PREDICTING THE UNPREDICTABLE!; 1. CHAOS: AN ILLUSTRATIVE EXAMPLE; 2. ALGORITHMIC COMPLEXITY THEORY; 3. ALGORITHMIC INTEGRABILITY; 4. ALGORITHMIC RANDOMNESS; 5. QUANTUM CHAOS, IF ANY?; REFERENCES; CHAPTER 2. MAKING CHAOTIC DYNAMICAL SYSTEMS TO ORDER; ABSTRACT; 1. INTRODUCTION; 2. THE COLLAGE THEOREM; 3. MAKING DIFFERENTIAL EQUATIONS WITH PRESCRIBED ATTRACTORS; REFERENCESCHAPTER 3. ON THE EXISTENCE AND NON-EXISTENCE OF NATURAL BOUNDARIES FOR NON-INTEGRABLE DYNAMICAL SYSTEMSABSTRACT; 1. INTRODUCTION; 2. NONLINEAR DIFFERENTIAL EQUATIONS AND ALGEBRAIC INTEGRABILITY; 3. A CANONICAL EXAMPLE; 4. SOME SIMPLE EXAMPLES; ACKNOWLEDGMENT; REFERENCES; CHAPTER 4. THE HENON MAPPING IN THE COMPLEX DOMAIN; 1. INTRODUCTION; 2. HISTORY AND MOTIVATION; 3. THE RELATION WITH THE THEORY OF POLYNOMIALS; 4. RATES OF ESCAPE FOR THE HENON FAMILY; 5. ANGLES OF ESCAPE; 6. A PROGRAM FOR DESCRIBING MAPPINGS IN THE HENON FAMILY; CHAPTER 5. DYNAMICAL COMPLEXITY OF MAPS OF THE INTERVAL1. THE ŠARKOVSKII STRATIFICATION2. TOPOLOGICAL ENTROPY; 3. TURBULENCE; 4. ENTROPY MINIMAL ORBITS; 5. HOMOCLINIC ORBITS; ACKNOWLEDGEMENTS; REFERENCES; CHAPTER 6. A USE OF CELLULAR AUTOMATA TO OBTAIN FAMILIES OF FRACTALS; ABSTRACT; 1. A SHORT HISTORY OF CELLULAR AUTOMATA; 2. WHAT ARE CELLULAR AUTOMATA?; 3. RESCALING TO OBTAIN FRACTALS IN THE LIMIT; 4. WAYS OF OBTAINING SOME NUMBERS FROM THE LIMIT SETS; 5. CONCLUSIONS AND DISCUSSION; REFERENCES; Part II: Julia Sets; CHAPTER 7. EXPLODING JULIA SETS; ABSTRACT; 1. INTRODUCTION; 2. AN EXPLOSION IN THE EXPONENTIAL FAMILYCHAPTER 12. DIOPHANTINE PROPERTIES OF JULIA SETSChaotic Dynamics and FractalsNotes and reports in mathematics in science and engineering ;Volume 2.DynamicsCongressesChaotic behavior in systemsCongressesFractalsCongressesDynamicsChaotic behavior in systemsFractals515.3/5Barnsley M. F(Michael Fielding),1946-Demko Stephen G.MiAaPQMiAaPQMiAaPQBOOK9910829150503321Chaotic dynamics and fractals343956UNINA