Celestial Encounters: The Origins of Chaos and StabilityCelestial Encounters is for anyone who has ever wondered about the foundations of chaos. In 1888, the 34-year-old Henri Poincaré submitted a paper that was to change the course of science, but not before it underwent significant changes itself. "The Three-Body Problem and the Equations of Dynamics" won a prize sponsored by King Oscar II of Sweden and Norway and the journal Acta Mathematica, but after accepting the prize, Poincaré found a serious mistake in his work. While correcting it, he discovered the phenomenon of chaos. |
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Efni
A Great DiscoveryAnd a Mistake | 3 |
A WALK in PARIS | 4 |
NEWTONS INSIGHT | 7 |
A LANGUAGE for the LAWS of NATURE | 9 |
MODELS of REALITY | 13 |
MANIFOLD WORLDS | 18 |
THE nBODY PROBLEM | 20 |
KING OSCARS PRIZE | 23 |
ENCOUNTERS at a CONFERENCE | 112 |
FROM FOUR to FIVE BODIES | 113 |
THE END of a CENTURYS QUEST | 116 |
A SYMMETRIC DIGRESSION | 122 |
AN IDEA at DINNER | 123 |
Stability | 127 |
A LONGING for ORDER | 128 |
THE MARQUIS and the EMPEROR | 131 |
POINCARES ACHIEVEMENT | 27 |
LES MÉTHODES NOUVELLES | 30 |
FIXED POINTS | 31 |
FIRST RETURNS | 34 |
A GLIMPSE OF CHAOS | 37 |
PANDORAS BOX | 42 |
POINCARES MISTAKE | 44 |
A SURPRISING DISCOVERY | 48 |
Symbolic Dynamics | 51 |
ON THE BEACH AT RIO | 55 |
SMALES HORSESHOE | 60 |
SHIFTS on SYMBOLS | 65 |
SYMBOLS for CHAOS | 68 |
OSCILLATIONS and REVOLUTIONS | 73 |
A NEW SCIENCE? | 78 |
A SINGULAR MAN | 82 |
COLLISION or BLOWUP | 88 |
COMPUTER GAMES | 91 |
HOW to CATCH a RABBIT | 96 |
A MEASURE of SUCCESS | 101 |
REGULARIZING COLLISIONS | 104 |
CELESTIAL BILLIARDS | 106 |
MUSIC of the SPHERES | 135 |
ETERNAL RETURN | 139 |
PERTURBING the WORLD | 143 |
How STABLE is STABLE? | 147 |
LINEARIZATION and ITS LIMITS | 153 |
THE STABILITY of MODELS | 157 |
PLANETS in BALANCE | 159 |
KAM Theory | 164 |
SIMPLIFY and SOLVE | 165 |
QUASIPERIODIC MOTIONS | 170 |
PERTURBING the TORI | 174 |
LETTERS a LOST SOLUTION and POLITICS | 177 |
WORRYING at the PROOF | 182 |
TWIST MAPS | 187 |
A GIFTED STUDENT | 190 |
CHAOS DIFFUSES | 193 |
EPILOGUE | 201 |
Notes | 203 |
Bibliography | 213 |
225 | |
Aðrar útgáfur - View all
Celestial Encounters: The Origins of Chaos and Stability Florin Diacu,Philip Holmes Takmarkað sýnishorn - 2020 |
Celestial Encounters: The Origins of Chaos and Stability Florin Diacu,Philip Holmes Takmarkað sýnishorn - 1999 |
Celestial Encounters: The Origins of Chaos and Stability Florin Diacu,Philip Holmes Engin sýnishorn í boði - 1996 |