Celestial Encounters (eBook)

The Origins of Chaos and Stability

Florin Diacu, Philip J. Holmes (Autoren)

eBook Download: PDF

2020
Princeton University Press (Verlag)
978-0-691-22183-0 (ISBN)

Infos

Celestial Encounters is for anyone who has ever wondered about the foundations of chaos. In 1888, the 34-year-old Henri Poincare submitted a paper that was to change the course of science, but not before it underwent significant changes itself. "e;The Three-Body Problem and the Equations of Dynamics"e; won a prize sponsored by King Oscar II of Sweden and Norway and the journal Acta Mathematica, but after accepting the prize, Poincare found a serious mistake in his work. While correcting it, he discovered the phenomenon of chaos. Starting with the story of Poincare's work, Florin Diacu and Philip Holmes trace the history of attempts to solve the problems of celestial mechanics first posed in Isaac Newton's Principia in 1686. In describing how mathematical rigor was brought to bear on one of our oldest fascinations--the motions of the heavens--they introduce the people whose ideas led to the flourishing field now called nonlinear dynamics. In presenting the modern theory of dynamical systems, the models underlying much of modern science are described pictorially, using the geometrical language invented by Poincare. More generally, the authors reflect on mathematical creativity and the roles that chance encounters, politics, and circumstance play in it.

Produkt-Details

• Erscheint lt. Verlag: 8.12.2020
• Reihe/Serie: Princeton Science Library
• Reihe/Serie: Princeton Science Library
• Zusatzinfo: 23 halftones 64 line illus.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Astronomie / Astrophysik
• Schlagworte: acceleration • Acta Mathematica • Addition • Alekseev, V. M. • American Mathematical Society • Analogy • Andrey Kolmogorov • Applied mathematics • Approximation • Arbitrarily large • Arnold diffusion • Asteroid • Astronomy • asymptotic analysis • Benjamin Pierce lecturer • Bifurcation Theory • Brown, Scott • Bureau des longitudes • Calculation • Calculus of Variations • Cantor set • Career • Carl Ludwig Siegel • Catastrophe Theory • Celestial mechanics • Center of mass (relativistic) • chaos theory • classical mechanics • close encounter • Complex Analysis • Computation • conjecture • conservation law • Constant of motion • coordinate system • degrees of freedom • Degrees of freedom (statistics) • Derivative • differential equation • Differential Geometry • Dimension • Dimension Theory • Dynamical system • eccentricity • Ecology • Elasticity (theory) • Ellipse • Elliptic orbit • Equation • Equilibrium Point • fields medal • First return map • Fixed point • Four-body problem • Function • general knowledge • Geometry • Gerver, Joseph • Gravitation • Gravity • Harvard University • Hirsch, Morris • Homoclinic orbit • Hopf Bifurcation • Horseshoe map • hypothesis • idealization • Incompressible Flow • Independent integrals • Initial Condition • instability • Instant • Inverse iteration • Isoperimetric property • Isosceles problem • Iteration • Jacques Hadamard • Jacques Laskar • Jones, Vaughan • KAM Theory • Karl Weierstrass • Kovalevskaia top • Lagrangian solutions • Lebesgue measure • Lecture • Legion of Honor • Leopold Kronecker • Lewis Institute • linear differential equation • Linearization • Line segment • Major axis • manifold • mathematician • Mathematics • Mendelian laws • Mercury • Mittag-Leffler Institute • Modern Physics • Momentum • Morrison Prize • N-Body Problem • New York University • Niles Eldredge • nonlinear system • Number Theory • operator theory • Orbit • Oscillation • Panthéon • Parameter • partial differential equation • pendulum • Periodic function • periodic point • Perturbation theory (quantum mechanics) • Phase space • Physical space • physicist • Probability • Probability Theory • Pure Mathematics • Quantity • quantum mechanics • result • saddle • Saddle point • Scientist • Sequence • Series expansion • Special case • Stephen Smale • Structural Stability • Summation • symbolic dynamics • Systems Theory • Theogony • Theorem • theory • Three-body problem • Three-dimensional space (mathematics) • Time • Topology • two-body problem • two-dimensional space • Variable (mathematics)
• ISBN-10: 0-691-22183-9 / 0691221839
• ISBN-13: 978-0-691-22183-0 / 9780691221830