By Bertrand Duplantier, Vincent Rivasseau

ISBN-10: 303480833X

ISBN-13: 9783034808330

This 13th quantity of the Poincaré Seminar sequence, *Henri Poincaré, 1912-2012*, is released at the get together of the centennial of the dying of Henri Poincaré in 1912. It offers a scholarly method of Poincaré’s genius and creativity in mathematical physics and arithmetic. Its 5 articles also are hugely pedagogical, as befits their starting place in lectures to a vast medical viewers. Highlights contain “Poincaré’s mild” via Olivier Darrigol, a number one historian of technology, who makes use of gentle as a guiding thread via a lot of Poincaré ’s physics and philosophy, from the appliance of his more advantageous mathematical talents and the idea of diffraction to his next reflections at the foundations of electromagnetism and the electrodynamics of relocating our bodies; the authoritative “Poincaré and the Three-Body challenge” by means of Alain Chenciner, who bargains an exquisitely special, hundred-page point of view, peppered with bright excerpts from citations, at the huge paintings of Poincaré in this topic, from the recognized (King Oscar’s) 1889 memoir to the rules of the trendy concept of chaos in “Les méthodes nouvelles de los angeles mécanique céleste.” A profoundly unique and scholarly presentation of the paintings through Poincaré on chance idea is given via Laurent Mazliak in “Poincaré’s Odds,” from the incidental first visual appeal of the observe “probability” in Poincaré’s recognized 1890 theorem of recurrence for dynamical structures, to his later reputation of the unavoidability of likelihood calculus in technology, as constructed to an exceptional quantity by way of Emile Borel, Poincaré’s major direct disciple; the thing through Francois Béguin, “Henri Poincaré and the Uniformization of Riemann Surfaces,” takes us on a desirable trip in the course of the six successive types in twenty-six years of the distinguished uniformization theorem, which exemplifies the Master’s unique signature within the foundational fusion of arithmetic and physics, on which conformal box idea, string conception and quantum gravity quite a bit count these days; the ultimate bankruptcy, “Harmony and Chaos, at the determine of Henri Poincaré” through the filmmaker Philippe Worms, describes the homonymous poetical movie within which eminent scientists, via mathematical scenes and actual experiments, demonstrate their emotional courting to the customarily elusive clinical fact and common “harmony and chaos” in Poincaré’s legacy.

This e-book could be of vast normal curiosity to physicists, mathematicians, philosophers of technology and historians.

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**Extra resources for Henri Poincaré, 1912-2012: Poincaré Seminar 2012**

**Sample text**

For an observer moving at the velocity u of the emitter, the recoil force does not work, and the spent energy S is obviously the same. According to the Lorentz transformations for time and ﬁelds (to ﬁrst order), this observer should ascribe the energy J (1 − u/c) to the emitted radiation and the value (−J/c)(1 − u/c) to the recoil momentum. Hence the energy principle is satisﬁed for the moving observer, but the (time integral of the) electromagnetic force acting on the emitter is modiﬁed by Ju/c2 .

25 At the very end of his lectures of 1887–88, Poincar´e summarized these results and noted that the conditions for the validity of Kirchhoﬀ’s approximation were no longer met. The true boundary conditions at the surface of the diﬀracting screen had to be taken into account, so that, pace Stokes, none of these experiments could decide between Fresnel’s and Neumann’s choice of the direction of vibration:26 This disagreement with Mr. Gouy’s experiments should not surprise us, for we have said that it was impossible to ﬁnd a solution of the equation Δξ + α2 ξ = 0 that satisﬁed exactly the conditions of the problem.

31, 323 (redrawn). the earth, and α a numerical constant. 32 In 1911, an American student of Sommerfeld, Herman William March, ﬁled a dissertation on the propagation of telegraphic waves around the earth and obtained results contradicting Poincar´e’s. In a letter to Sommerfeld and in a note to the Compte rendus, Poincar´e identiﬁed a fatal error in March’s calculation. He also noted that a Trinity Wrangler, John William Nicholson, had conﬁrmed his own exponential law. 696) for the numerical coeﬃcient α in Poincar´e’s law.

### Henri Poincaré, 1912-2012: Poincaré Seminar 2012 by Bertrand Duplantier, Vincent Rivasseau

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Categories: Mathematical Physics