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Systèmes dynamiques avec Poincaré

Author Aurelien Alvarez
Translator Dr. Rashid Barhoun
Publish Year
ISBN 9789948135227
Price AED 95
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The Dynamic Systems book was published with Henri Poincaré in the "Mathematical Journeys," series on the 100th anniversary of Poincaré's death. It is noteworthy that this scientist is considered the greatest mathematician of the 19th century. At the same time,, the book discusses certain aspects of his character and his contributions, which we may refer to as an academic biography. This book also helps us discover two sides of his life which were not previously invoked. The first aspect is that of the intellectual who fights for a cause he believes in and which is closely related to his own vision of science. The second is related to his relation to societal issues, in reference to the significant and conclusive role he played in the case of Officer Dreyfus. The author also informs us that Poincaré's relationship to the aforementioned mentioned case took place at a time when the idea that the intellect could form a new, key actor on the social and political spectrum was borne. This raises several questions tied to the intersection between science and society, relationships between scientific practices and citizen awareness, and the status of science in democratic nations. The book also discusses questions related to scientists' tendency to intervene in social causes, the ethics of the scientist, and the independence of science.  From psychology and topics related to politics and science, we move on to a game that nobody expected to find among books that discuss physics and mathematics: billiards. The book evokes the game in the context of its relationship to the dynamic system and its functionality in various dimensions. This game constitutes a rich example for dynamic systems which study celestial mechanics as well, in particular the Three-Body Problem. This was initiated by a question combining both systems: can we predict the location to which a billiard ball will rebound? In the same fashion, can earth's location - after the passage of hundreds of thousands of years - be predicted? A mathematician does not claim to read the future. They asks questions, phrasing hypotheses and proofs. This is precisely what we will discover during our journey into mathematics with Henri Poincaré.