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Entropy2016,18, 370 19. Newton, I.PhilosophiaNaturalisPrincipiaMathematica;Translated inFrenchbyÉmilieduChastelet (1756); London,UK,1687. (InFrench) 20. Lagrange, J.L.MécaniqueAnalytique, 1st ed.; LaveuvedeSaint-Pierre: Paris, France, 1808; reprintedby JacquesGabay: Paris,France,1989. (InFrench) 21. Hamilton,W.R.On ageneralmethod inDynamics. InSirWilliamRowanHamiltonMathematicalWorks, VolumeII;CambridgeUniversityPress:Cambridge,UK,1940;pp.247–308. 22. Hamilton,W.R.SecondessayonageneralmethodinDynamics. InSirWilliamRowanHamiltonMathematical Works,VolumeII;CambridgeUniversityPress:Cambridge,UK,1940;pp.95–144. 23. Bérest,P.CalculdesVariationsApplicationà laMécaniqueet à laPhysique;Ellipses/ÉditionsMarketing: Paris, France,1997. (InFrench) 24. Bourguignon, J.-P.CalculVariationnel;Éditionsde l’ÉcolePolytechnique: Paris,France,1991. (InFrench) 25. Lanczos, C.S. The Variational Principles of Mechanics, 4th ed.; Reprinted by Dover, New York, 1970; UniversityofTorontoPress: Toronto,ON,Canada,1970. 26. Malliavin,P.GéométrieDifférentielle Intrinsèque;ÉditionsHermann: Paris,France,1972. (InFrench) 27. Sternberg,S.LecturesonDifferentialGeometry;Prentice-Hall:UpperSaddleRiver,NJ,USA,1964. 28. Kosmann-Schwarzbach,Y.TheNoetherTheorems; Springer: Berlin/Heidelberg,Germany,2011. 29. Poincaré,H.Suruneformenouvelledeséquationsde laMéanique.C.R.Acad.Sci. 1901,7, 369–371. 30. Marle,C.-M.OnHenriPoincaré’snote“Suruneformenouvelledeséquationsde laMécanique”. J.Geom. SymmetryPhys. 2013,29, 1–38. 31. Barbaresco,F.Symplectic structureof informationgeometry: Fishermetricandeuler-poincaréequationof souriau lie group thermodynamics. In Geometric Science of Information: Second International Conference, GSI 2015, Proceedings; Nielsen, F., Barbaresco, F., Eds.; Lecture Notes in Computer Science; Springer: Berlin/Heidelberg,Germany,2015;Volume9389,pp. 529–540. (InFrench) 32. Lagrange, J.-L.Mémoire sur laThéorieGénéralede laVariationdesConstantesArbitrairesDansTous lesProblèmes deMécanique; Lu le13mars1809à l’InstitutdeFrance;DansŒuvresdeLagrange;Gauthier-Villars: Paris, France,1877;VolumeVI,pp. 771–805. (InFrench) 33. Lagrange, J.-L.SecondMémoire sur laThéorie de laVariationdesConstantesArbitrairesDans lesProblèmesde Mécanique;Gauthier-Villars: Paris,France,1877;VolumeVI,pp. 809–816. (InFrench) 34. Tulczyjew,W.M.Hamiltoniansystems,LagrangiansystemsandtheLegendre transformation.Symp.Math. 1974,14, 247–258. 35. Tulczyjew,W.M.GeometricFormulationsofPhysicalTheories;MonographsandTextbooks inPhysicalScience; Bibliopolis:Napoli, Italy,1989. 36. Lichnerowicz,A.LesvariétésdePoissonet leursalgèbresdeLieassociées. J.Differ. Geom. 1977,12, 253–300. (InFrench) 37. Lichnerowicz,A.Lesvariétésde Jacobi et leurs algèbresdeLie associées. J.Math. PuresAppl. 1979, 57, 453–488. (InFrench) 38. Kirillov,A. Local liealgebras.Russ.Math. Surv. 1976,31, 55–75. 39. Poisson, S.D.Sur lavariationdesconstantesarbitrairesdans lesquestionsdemécanique. Mémoire lu le 16octobre1809à l’InstitutdeFrance. JournaldeL’ÉcolePolytechniquequinzièmecahier, tomeVIII, 266–344. (InFrench) 40. Koszul, J.-L.CrochetdeSchouten-Nijenhuiset cohomologie. InÉ.Cartanet lesMathématiquesD’aujourd’hui; Astérisque,numérohorssérie,SociétéMathématiquedeFrance: Paris,France,1985;pp. 257–271. (InFrench) 41. Marle,C.-M.CalculusonLiealgebroids,LiegroupoidsandPoissonmanifolds.DissertationesMathematicae 457, Institute ofMathematics,PolishAcademyofSciences (Warszawa). 2008, arXiv:0806.0919. 42. Weinstein,A.The local structureofPoissonmanifolds. J.Differ. Geom. 1983,18, 523–557. 43. Marsden, J.E.;Weinstein,A.Reductionofsymplecticmanifoldswithsymmetry.Rep.Math. Phys. 1974,5, 121–130. 44. Meyer,K.Symmetriesandintegrals inmechanics. InDynamicalSystems;Peixoto,M.,Ed.;AcademicPress, NewYork,NY,USA,1973;pp.259–273. 45. DeSaxcé,G.;Vallée,C.GalileanMechanics andThermodynamicsofContinua; JohnWiley&Sons:Hoboken,NJ, USA,2016. 46. Boltzmann,L.E.Leçonssur laThéoriedesgaz.Availableonline: http://iris.univ-lille1.fr/handle/1908/1523 (accessedon11October2016). (InFrench) 47
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Differential Geometrical Theory of Statistics
Title
Differential Geometrical Theory of Statistics
Authors
Frédéric Barbaresco
Frank Nielsen
Editor
MDPI
Location
Basel
Date
2017
Language
English
License
CC BY-NC-ND 4.0
ISBN
978-3-03842-425-3
Size
17.0 x 24.4 cm
Pages
476
Keywords
Entropy, Coding Theory, Maximum entropy, Information geometry, Computational Information Geometry, Hessian Geometry, Divergence Geometry, Information topology, Cohomology, Shape Space, Statistical physics, Thermodynamics
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