Publications

Sergio Benenti

November 3, 2014

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• 87 S.Benenti, Meccanica dei sistemi anolonomi, Capitolo 11 del volumeComplementi alle Lezioni di Meccanica Razionale di T. Levi-Civita e U. Amaldi,ed. Compomat, 2012, p.213-257.

• 86 S.Benenti, The non-holonomic double pendulum, an example of non-linear non-holonomic system, Regul. Chaotic Dyn., 2011, 16 (5), pp. 417-442.

• 85 S.Benenti, Hamiltonian structures and Generating Families, Springer,Universitext, 2011.

• 84 S.Benenti, Hamiltonian structures and Generating Families (in Rus-sian), 2009.

• 83 S.Benenti, A general method for writing the dynamical equations ofnonholonomic systems with ideal constraints. Regular and Chaotic Dynamics(R&C Dynamics), 2008, Vol. 13, No.4, pp. 283-315. Pleiades Publishing,Ltd., 2008.

• 82 S.Benenti, Computing curvature without Christoffel symbols. SPT2007Proceedings, Symmetry and Perturbation Theory, Otranto, Italy, 2-9 June2007, G. Gaeta, R. Vitolo, S. Walcher Eds., World Scientific 2008, 37-44.

• 81 S.Benenti, A user-friendly approach to the dynamics of non-holonomicsystems. SIGMA 3 (2007), 036, 33 pages.

http://www.emis.de/journals/SIGMA/.

• 80 S.Benenti, Algebraic construction of the quadratic first integrals for aspecial class of orthogonal separable systems. IMA Volumes in Mathematicsand Its Applications, Volume 114: Symmetries and Overdetermined Systems

of Partial Differential Equations. Editors: Michael Eastwood and WillardMiller, Jr.. Springer 2007.

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• 79 S.Benenti, The Lagrangian and Hamiltonian formulations for a specialclass of non-conservative systems. ”Symmetry and Perturbation Theory - SPT2004” (proceedings of the conference held in Cala Gonone, 19-26 May 2002),S. Abenda, G. Gaeta, S. Walcher Eds., World Scientific 2005, 43-50.

• 78 S.Benenti, Special symmetric two-tensors, equivalent dynamical sys-tems, cofactor and bi-cofactor systems. Acta Applicandae Mathematicae 87

(2005), 33-91.

• 77 S.Benenti, Torsionless conformal Killing tensors and cofactor-pair sys-tems. Lecture at the International Conference State of-the-art in the separa-

bility theory for the differential equations, Department of Mathematics, Uni-versity of Linkoping, January 6-11, 2004, organized by K. Marciniak and S.Rauch-Wojciechowski. Unpublished.

• 76 S.Benenti, C.Chanu, G.Rastelli, Variable separation theory for thenull Hamilton-Jacobi equation. J. Math. Phys. 46 (4), 2901-2930 (2005).

• 75 S. Benenti, Separability on Riemannian manifolds (2004). Unpublished.Available at the web page http://www2.dm.unito.it/∼benenti/ .

• 74 S.Benenti, Hamiltonian Optics and Generating Families. Napoli Serieson Physics and Astrophysics, Bibliopolis, Naples (2003).

• 73 S. Benenti, On the correspondence between classical and quantum ob-servables (A naive approach to the exact quantization problem). In Advancesin General Relativity and Cosmology (June, 2002). In memory of A. Lich-nerowicz, G. Ferrarese Ed., Pitagora Editrice, Bologna 2003, 85-108.

• 72 S. Benenti, An outline of the geometrical theory of the separation ofvariables in the Hamilton-Jacobi and Schrodinger equations. ”Symmetry andPerturbation Theory - SPT 2002” (proceedings of the conference held in CalaGonone, 19-26 May 2002), S. Abenda, G. Gaeta, S. Walcher Eds., WorldScientific 2002, 1-17.

• 71 S.Benenti, C.Chanu, G.Rastelli, Remarks on the connection be-tween the additive separation of the Hamilton-Jacobi equation and the multi-plicative separation of the Schrodinger equation. II. First integrals and sym-metry operators. J. Math. Phys. 43 (11), 5223-5253 (2002).

• 70 S.Benenti, C.Chanu, G.Rastelli, Remarks on the connection be-tween the additive separation of the Hamilton-Jacobi equation and the multi-plicative separation of the Schrodinger equation. I. The completeness and theRobertson conditions. J. Math. Phys. 43 (11), 5183-5222 (2002).

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• 69 S.Benenti, C.Chanu, G.Rastelli, Variable separation for naturalHamiltonians with scalar and vector potentials. J. Math. Phys. 42 (5), 2065-2091 (2001).

• 68 S.Benenti, C.Chanu, G.Rastelli, The super-separability of the three-body inverse-square Calogero system. J. Math. Phys. 41 (7), 4654-4678 (2000).

• 67 S.Benenti, Geometrical aspects of the dynamics of non-holonomic sys-tems. Rend. Semin. Matem. Univ. Polit. Torino 54 (3), 203-212 (1996) –reprint of [45].

• 66 S.Benenti, Intrinsic characterization of the variable separation in theHamilton-Jacobi equation, J. Math. Phys. 38 (12), 6578-6602 (1997).

• [65] S.Benenti, R.Monaco, Calcolo differenziale per le scienze applicate -Analisi delle funzioni ad una variabile reale. Celid, Torino (1997).

• [64] S.Benenti, Modelli matematici della meccanica II - Lagrange, Hamilton,Einstein. Celid, Torino (1997).

• [63] S.Benenti, Modelli matematici della meccanica I - Sistemi dinamici,Cinematica, Meccanica newtoniana. Celid, Torino (1997).

• [62]E.G.Kalnins, S.Benenti, W.Miller Jr., Integrability, Stackel spaces,and rational potentials, J. Math. Phys. 38 (5), 2345-2365 (1997).

• [61] S.Benenti, Connections and Hamiltonian Mechanics, ”Gravitation Elec-tromagnetism and Geometrical Structures”, G.Ferrarese Ed., 185-206, PitagoraEditrice Bologna (1996).

• [60] S.Benenti, Lezioni di Meccanica Razionale, Parte II, CLU, Torino (1995).

• [59] S.Benenti, Meccanica analitica, ”Enciclopedia Treccani delle ScienzeFisiche” (1994).

• [58] S.Benenti, Lezioni di Meccanica Razionale, Parte I, CLU, Torino (1994).

• [57] S.Benenti, Elementi di Meccanica Analitica, Parte I, CLU, Torino (1994).

• 56 S.Benenti, Orthogonal separable dynamical systems, in ”DifferentialGeometry and Its Applications”, Vol. I, Proceedings of the 5th InternationalConference on Differential Geometry and Its Applications, Silesian Universityat Opava, August 24-28, 1992, O.Kowalski and D.Krupka Eds., 163-184 (1993).Electronic edition: ELibEMS, http://www.emis.de/proceedings/.

• 55 S.Benenti, Inertia tensors and Stackel systems in the Euclidean spaces,Rend. Semin. Mat. Univ. Polit. Torino, 50, 315-341 (1992).

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• [54] S.Benenti, O.Bogoyavlenskii, Integrable Lagrangian systems on qua-drics with additional symmetries. Atti Accad. Sci. Torino 126, 187-196 (1992).

• 53 S.Benenti, Orthogonal separation of variables on manifolds with con-stant curvature. Diff. Geom. Appl. 2, 351-367 (1992).

• 52 S.Benenti, Separation of variables in the geodesic Hamilton-Jacobi equa-tion. Progress in Mathematics 99, 1-36 (1991).

• [51] S.Benenti, G.Rastelli, Sistemi di coordinate separabili nel piano eu-clideo. Memorie Accad. Sci. Torino 15 (1-2), 1-21 (1991).

• [50] S.Benenti, Stackel systems and Killing tensors. Note Matem. 9 (Suppl.),39-58 (1989).

• 49 S.Benenti, L’integration de l’equation d’Hamilton-Jacobi par separationdes variables: histoire et resultats recents. Colloque ”La Mecanique Analy-tique de Lagrange et son heritage”, Fondation Hugot du College de France,Paris, 27-29 septembre 1988. Atti dell’Accademia delle Scienze di Torino 124,119-144 (1990).

• [48] S.Benenti, On the orthogonality of the second class coordinates in theseparation of the Hamilton-Jacobi equation. Atti Accad. Sci. Torino 123,167-171 (1989).

• [47] S.Benenti, Relazioni simplettiche: la trasformazione di Legendre e lateoria di Hamilton-Jacobi. Quaderni dell’Unione Matematica Italiana 33,Pitagora Editrice, Bologna (1988).

• [46] S.Benenti, W.M.Tulczyjew, Canonical affine bundles. Atti Accad.Sci. Torino 122, 89-100 (1988).

• [45] S.Benenti, Geometrical aspects of the dynamics of non-holonomic sys-tems. in Journees Relativistes 1987, Chambery, 14-16 mai 1987, Universite deSavoie, Departement de Mathematiques.

• [44] S.Benenti, G.Pidello, Sulla formulazione hamiltoniana della mecca-nica dei sistemi con vincoli non-olonomi. In Scritti vari di Fisica Matematica

dedicati a C. Agostinelli, Accademia delle Scienze di Torino, 45-51 (1987).

• [43] S.Benenti, Fibres affines canoniques et mecanique newtonienne. ActionHamiltonienne de Groupes, P.Dazord, N.Desolneux-Moulis, J.M.Morvan Eds.,Travaux en Cours 27, Hermann, Paris, 13-38 (1987).

• [42] S.Benenti, W.M.Tulczyjew, Cocycles of the coadjoint representationof a Lie group interpreted as differential forms. Mem. Accad. Sci. Torino 10,117-138 (1986).

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• [41] S.Benenti, W.M.Tulczyjew, A geometrical interpretation of the 1-cocycles of a Lie group. Geometrodynamics, A.Prastaro Ed., World ScientificPublishing Co., 3-24 (1985).

• [40] S.Benenti, W.M.Tulczyjew , Sur un feuilletage coisotrope du fibrecotangent d’un groupe de Lie. C.R.A.S. Paris 300, 119-122 (1985).

• [39] S.Benenti, W.M.Tulczyjew, Momentum relations for Hamiltonianactions. In Geometrie Symplectique et Mecanique, J.P.Dufour Ed., Travauxen Cours, Hermann, Paris, 12-29 (1985).

• [38] S.Benenti, Homogeneous formulation of Hamiltonian group actions. 4thMeeting on Mathematical Physics, University of Coimbra, October 15-16, 1984(unpublished note).

• [37] S.Benenti, The Hamilton-Jacobi equation for a Hamiltonian action, Ge-ometrodynamics Procceedings 1983, A.Prastaro Ed., Pitagora Editrice, Bologna(1984) 1-15.

• [36] S.Benenti, G.Pidello, Separability structures corresponding to con-servative dynamical systems. Meccanica 19 (1984), 275-281.

• [35] S.Benenti The category of symplectic reductions, Proceedings of theInternational Meeting on Geometry and Physics, Florence, October 12-15,1992, Pitagora Editrice, Bologna (1993), 11-41.

• [34] S.Benenti, Linear symplectic relations. Symplectic Geometry, A.Cru-meyrolle & J.Grifone Eds., Research Notes in Math. 80, Pitman (1983).

• [33] S.Benenti, Symplectic relations in Analytical Mechanics. ProceedingsIUTAM-ISIMM Symposium on ”Modern Developments in Analytical Mechan-ics”, Turin, June 7-11, 1982, Atti Accad. Sci. Torino, 117 (suppl., 1993), 39-91.

• 32 S.Benenti, W.M.Tulczyjew, Sur le theoreme de Jacobi en mecaniqueanalytique. C.R.A.S. Paris 294, 677-680 (1982).

• [31] S.Benenti, Concetti e risultati principali della teoria delle strutture diseparabilita su varieta riemanniane, Atti III Convegno Nazionale di Relativitae Fisica della Gravitazione, Torino 1978, Accademia delle Scienze di Torino,181-187 (1981).

• 30 S.Benenti, W.M.Tulczyjew, Remarques sur les reductions symplec-tiques, C.R.A.S. Paris 294, 561-564 (1982).

• 29 S.Benenti, Separability structures on Riemannian manifolds. L.N.Math.863, 512-538 (1980).

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• [28] S.Benenti, W.M.Tulczyjew, The geometrical meaning and globaliza-tion of the Hamilton-Jacobi method. in L.N.Math. 863, 9-21 (1980).

• [27] S.Benenti, M.Francaviglia, Canonical forms for separability struc-tures with less than five Killing tensors. Ann. Inst. H. Poincare 34, 45-64(1981).

• [26] S.Benenti, W.M.Tulczyjew, Geometry of static mechanical systemswith constraints. Ann. Mat. Pura Appl. 124, 139-160 (1980).

• [25] S.Benenti, M.Francaviglia, The theory of separability of the Hamilton-Jacobi equation and its applications to general relativity. General Relativity

and Gravitation, A.Held Ed., Plenum, Vol. 1 393-439 (1980).

• 24 S.Benenti, Structures de separabilite sur une variete riemannienne designature quelconque. C. R. A. S. Paris 289, 795-798 (1979).

• [23] S.Benenti, M.Francaviglia, Canonical forms of Sn−3−structures inpseudo-Riemannian manifolds. Ann. Inst. H. Poincare 30, 143-157 (1979).

• [22] S.Benenti, M.Francaviglia, Remarks on certain separability struc-tures and their applications to general relativity. GRG Journal 10, 79-82(1979).

• [21] S.Benenti, W.M.Tulczyjew, Relazioni lineari simplettiche. MemorieAccad. Sci. Torino 5, 71-140 (1979).

• [20] S.Benenti, W.M.Tulczyjew, Relazioni lineari binarie tra spazi vetto-riali di dimensione finita. Memorie Accad. Sci. Torino 3, 67-113 (1979).

• 19 S.Benenti, W.M.Tulczyjew, Sur l’existence du potentiel pour lessystemes mecaniques avec des liaisons non holonomes. C.R.A.S. Paris 286,237-240 (1978).

• 18 S.Benenti, Integrabilita per separazione delle variabili delle equazionialle derivate parziali lineari del secondo ordine interessanti la fisica-matematica.Atti Accad. Naz. Lincei 62, 51-60 (1977).

• 17 S.Benenti, Separable dynamical systems: Characterization of separa-bility structures on Riemannian manifolds. Rep. Math. Phys. 12, 311-316(1977).

• [16] S.Benenti, Proprieta intrinseche dei sistemi dinamici separabili e con-dizioni necessarie per l’integrabilita dell’equazione di Hamilton-Jacobi me-diante separazione delle variabili. Atti III Congresso Nazionale AIMETA,Cagliari 13-16 ottobre 1976, I - 10.1, 10.12.

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• 15 S.Benenti, Sur les structures de separabilite des varietes riemanniennes.C.R.A.S. Paris 283, 215-218 (1976).

• [14] S.Benenti, Strutture di separabilita su varieta riemanniane. Rend. Sem.Mat. Univ. Polit. Torino 34, 431-463 (1975-76).

• [13] S.Benenti, Sulle isometrie identiche su sottospazi di codimensione due.Rend. Semin. Matem. Univ. Polit. Torino 34, 333-339 (1975-76).

• [12] S.Benenti, Sulla struttura riemanniana delle varieta delle configurazionidi un corpo rigido con un punto fisso. Atti Accad. Sci. Torino 110, 245-256(1975-76).

• [11] S.Benenti, Sui cambiamenti di riferimento in relativita ristretta. AttiAccad. Sci. Torino 110, 125-133 (1975-76).

• [10] S.Benenti, Su di una particolare classe di rotazioni negli spazi quadridi-mensionali non minkowskiani. Atti Accad. Sci. Torino 109, 493-497 (1974-75).

• [9] S.Benenti, Sull’algebra di Clifford e sulla struttura tensoriale delle ro-tazioni in uno spazio vettoriale reale a quattro dimensioni. Rend. Semin.Matem. Univ. Polit. Torino 33, 73-102 (1974-75).

• [8] S.Benenti, Sulla generalizzazione del vettore caratteristico delle rotazioninei moti rigidi. Rend. Semin. Matem. Univ. Polit. Torino 32, 405-423 (1973-74).

• [7] S.Benenti, Sulla deformazione di una verga a nove parametri. Rend.Semin. Matem. Univ. Polit. Torino 31, 243-260 (1972-73).

• [6] S.Benenti, Sulla rappresentazione tramite tensori emisimmetrici di op-eratori ortogonali in uno spazio tridimensionale. Rend. Circ. Metm. Palermo22, 257-288 (1973).

• [5] S.Benenti, Forme canoniche degli operatori ortogonali in uno spazio tridi-mensionale. Rend. Circ. Matem. Palermo 22, 113-127 (1973).

• [4] S.Benenti, Sulla meccanica delle verghe sottili: schemi speciali. Rend.Matem. 5-VI, 159-179 (1972).

• [3] S.Benenti, Sulla meccanica delle verghe sottili a nove parametri. Rend.Matem. 4-VI, 705-722 (1971).

• [2] S.Benenti, Teorema dei moti relativi e di Coriolis in relativita generale.Rend. Semin. Matem. Univ. Polit. Torino 28, 115-133 (1968-69).

• [1] S.Benenti, Accelerazione relativa e derivazione vincolata ad un genericoriferimento fisico in relativita generale. Rend. Matem. 2-VI, 235-244 (1969).

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