By Radu, Dragos Hrimiuc, Kideo Shimada and Sorin V. Sabau Miron
The identify of this ebook is not surprising for individuals operating within the box of Analytical Mechanics. notwithstanding, the geometric suggestions of Lagrange house and Hamilton area are thoroughly new. The geometry of Lagrange areas, brought and studied in ,, was once ext- sively tested within the final 20 years by way of geometers and physicists from Canada, Germany, Hungary, Italy, Japan, Romania, Russia and U.S.A. Many overseas meetings have been dedicated to debate this topic, lawsuits and monographs have been released , , , ,... a wide quarter of applicability of this geometry is advised via the connections to Biology, Mechanics, and Physics and likewise through its normal surroundings as a generalization of Finsler and Riemannian geometries. the concept that of Hamilton area, brought in ,  was once intensively studied in , , ,... and it's been profitable, as a geometrical idea of the Ham- tonian functionality the basic entity in Mechanics and Physics. The classical Legendre’s duality makes attainable a ordinary connection among Lagrange and - miltonspaces. It finds new suggestions and geometrical gadgets of Hamilton areas which are twin to these that are comparable in Lagrange areas. Following this duality Cartan areas brought and studied in , ,..., are, approximately talking, the Legendre duals of convinced Finsler areas , , . The above arguments make this monograph a continuation of , , emphasizing the Hamilton geometry.