LEADER 03653nam 2200613 450 001 9910786639803321 005 20230120014648.0 010 $a1-4832-6908-6 035 $a(CKB)3710000000200396 035 $a(EBL)1901513 035 $a(SSID)ssj0001266574 035 $a(PQKBManifestationID)12564617 035 $a(PQKBTitleCode)TC0001266574 035 $a(PQKBWorkID)11249538 035 $a(PQKB)10838653 035 $a(MiAaPQ)EBC1901513 035 $a(EXLCZ)993710000000200396 100 $a20150202h19861986 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aChaotic dynamics and fractals /$fedited by Michael F. Barnsley, Stephen G. Demko 210 1$aOrlando, Florida ;$aLondon, England :$cAcademic Press, Inc.,$d1986. 210 4$dİ1986 215 $a1 online resource (305 p.) 225 1 $aNotes and Reports in Mathematics in Science and Engineering ;$vVolume 2 300 $aDescription based upon print version of record. 311 $a1-322-55828-0 311 $a0-12-079060-2 320 $aIncludes bibliographical references at the end of each chapters. 327 $aFront 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; REFERENCES 327 $aCHAPTER 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 INTERVAL 327 $a1. THE S?ARKOVSKII 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 FAMILY 327 $aCHAPTER 12. DIOPHANTINE PROPERTIES OF JULIA SETS 330 $aChaotic Dynamics and Fractals 410 0$aNotes and reports in mathematics in science and engineering ;$vVolume 2. 606 $aDynamics$vCongresses 606 $aChaotic behavior in systems$vCongresses 606 $aFractals$vCongresses 615 0$aDynamics 615 0$aChaotic behavior in systems 615 0$aFractals 676 $a515.3/5 702 $aBarnsley$b M. F$g(Michael Fielding),$f1946- 702 $aDemko$b Stephen G. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910786639803321 996 $aChaotic dynamics and fractals$9343956 997 $aUNINA