Xavier Gràcia: research publications

Research publications

M. de León, X. Gràcia, R. Izquierdo-López, Á. Martínez-Muñoz and X. Rivas
"Poisson and Jacobi structures from 2-covariant tensors"
arXiv: 2606.20030
X. Gràcia, Á. Martínez-Muñoz and X. Rivas
"Pairs of differential forms: a framework for precontact geometry"
arXiv: 2602.04882
X. Gràcia, Á. Martínez-Muñoz, X. Rivas and N. Román-Roy
"The evolution operator connecting the lagrangian and hamiltonian formalisms for contact systems"
Lett. Math. Phys. 116:67 (2026) (33 pp)
DOI: https://doi.org/10.1007/s11005-026-02093-5 arXiv: 2511.13401
X. Gràcia, X. Rivas and D. Torres
"Time-dependent metrics and connections"
Geom. Mech. 3 (2026) 91-112
DOI: https://dx.doi.org/10.1142/S2972458926400034 arXiv: 2601.14064
A. Martí, J. Riba, M. Lamarca and X. Gràcia
"Asymptotic analysis of near-field coupling in massive MISO and massive SIMO systems"
IEEE Commun. Lett. 28 (2024) 1929-1933
DOI: https://doi.org/10.1109/LCOMM.2024.3416044 arXiv: 2406.04786
X. Gràcia, J. de Lucas, X. Rivas and N. Román-Roy
"On Darboux theorems for geometric structures induced by closed forms"
Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 118, 131 (2024) (35 pp)
DOI: https://doi.org/10.1007/s13398-024-01632-w arXiv: 2306.08556
M. de León, J. Gaset, X. Gràcia, M.C. Muñoz-Lecanda and X. Rivas
"Time-dependent contact mechanics"
Monat. Math. 201 (2023) 1149-1183
DOI: https://doi.org/10.1007/s00605-022-01767-1 arXiv: 2205.09454
J. de Lucas, X. Gràcia, X. Rivas, N. Román-Roy and S. Vilariño
"Reduction and reconstruction of multisymplectic Lie systems"
J. Phys. A: Math. Theor. 55 (2022) 295204 (34 pp)
DOI: 10.1088/1751-8121/ac78ab arXiv: 2202.13748
X. Gràcia, X. Rivas and N. Román-Roy
"Skinner-Rusk formalism for k-contact systems"
J. Geom. Phys. 172 (2022) 104429 (24 pp)
DOI: 10.1016/j.geomphys.2021.104429 arXiv: 2109.07257
X. Gràcia
"Hamilton-Jacobi theory and geometric mechanics", pp. 35-41 in
Extended Abstracts GEOMVAP 2019,
edited by M. Alberich-Carramiñana et al.
Trends in Mathematics, vol. 15. Birkhäuser, Cham, 2021.
DOI: 10.1007/978-3-030-84800-2_6 ISBN: 978-3-030-84799-9 abstract
X. Gràcia, X. Rivas and N. Román-Roy
"Erratum: Constraint algorithm for singular field theories in the k-cosymplectic framework"
J. Geom. Mech. 13 (2021) 273-275
DOI: 10.3934/jgm.2021007
J. Gaset, X. Gràcia, M.-C. Muñoz-Lecanda, X. Rivas and N. Román-Roy
"A k-contact Lagrangian formulation for nonconservative field theories"
Rep. Math. Phys. 87 (2021) 347-368
DOI: 10.1016/S0034-4877(21)00041-0 arXiv: 2002.10458
J. Gaset, X. Gràcia, M.-C. Muñoz-Lecanda, X. Rivas and N. Román-Roy
"New contributions to the Hamiltonian and Lagrangian contact formalisms for dissipative mechanical systems and their symmetries"
Int. J. Geometric Methods in Mod. Phys. 17 (2020) 2050090 (27 pp)
DOI: 10.1142/S0219887820500905 arXiv: 1907.02947
J. Gaset, X. Gràcia, M.-C. Muñoz-Lecanda, X. Rivas and N. Román-Roy
"A contact geometry framework for field theories with dissipation"
Ann. Phys. 414 (2020) 168092 (20 pp)
DOI: 10.1016/j.aop.2020.168092 arXiv: 1905.07354
X. Gràcia, X. Rivas and N. Román-Roy
"Constraint algorithm for singular field theories in the k-cosymplectic framework"
J. Geom. Mech. 12 (2020) 1-23
DOI: 10.3934/jgm.2020002 arXiv: 1812.08487
X. Gràcia, J. de Lucas, M.-C. Muñoz-Lecanda and S. Vilariño
"Multisymplectic structures and invariant tensors for Lie systems"
J. Phys. A: Math. Theor. 52 (2019) 215201 (33 pp)
DOI: 10.1088/1751-8121/ab15f2 arXiv: 1808.06240
X. Gràcia and T. Sanz-Perela
"The wave equation for stiff strings and piano tuning"
Reports@SCM 3 (2017) 1-16
DOI: 10.2436/20.2002.02.11 arXiv: 1603.05516
J.F. Cariñena, E. Martínez, G. Marmo, X. Gràcia and M.-C. Muñoz-Lecanda
"A quantum route to Hamilton-Jacobi equation: comments and remarks", pp. 41-56 in
Geometry of Jets and Fields; in honour of Professor Janusz Grabowski,
edited by K. Grabowska, M. Jóźwikowski, J. de Lucas and M. Rotkiewicz.
Banach Center Publications vol. 110
Polish Academy of Sciences, Warszawa, 2016
DOI: 10.4064/bc110-0-3 ISBN: 978-83-86806-34-8 abstract
J.F. Cariñena, X. Gràcia, G. Marmo, E. Martínez, M.-C. Muñoz-Lecanda and N. Román-Roy
"Structural aspects of Hamilton-Jacobi theory"
Int. J. Geometric Methods in Mod. Phys. 13 (2016) 1650017 (29 pages)
DOI: 10.1142/S0219887816500171 arXiv: 1511.00288
J.F. Cariñena, X. Gràcia, G. Marmo, E. Martínez, M.-C. Muñoz-Lecanda and N. Román-Roy
"Geometric Hamilton-Jacobi theory for nonholonomic dynamical systems"
Int. J. Geometric Methods in Mod. Phys. 7 (2010) 431-454
DOI: 10.1142/S0219887810004385 arXiv: 0908.2453
X. Gràcia, R. Martín and N. Román-Roy
"Constraint algorithm for k-presymplectic hamiltonian systems. Application to singular field theories"
Int. J. Geometric Methods in Mod. Phys. 6 (2009) 851-872
DOI: 10.1142/S0219887809003795 arXiv: 0903.1791
J.F. Cariñena, X. Gràcia, E. Martínez, G. Marmo, M.-C. Muñoz-Lecanda and N. Román-Roy
"Hamilton-Jacobi theory and the evolution operator", pp. 177-186 in
Mathematical physics and field theory. Julio Abad, in memoriam
edited by M. Asorey, J.V. García Esteve, M.F. Rañada and J. Sesma
Prensas Universitarias de Zaragoza, 2009
ISBN: 978-84-92774-04-3 pdf arXiv: 0907.1039
X. Gràcia and R. Martín
"Vector hulls of affine spaces and affine bundles"
Acta Applicandae Mathematicae 103 (2008) 101-129
DOI: 10.1007/s10440-008-9222-6 abstract
J.F. Cariñena, X. Gràcia, G. Marmo, E. Martínez, M.-C. Muñoz-Lecanda and N. Román-Roy
"A new geometrical setting for the Hamilton-Jacobi equation", pp. 198-204 in
Proceedings of the XIV Fall Workshop on Geometry and Physics, Bilbao, 2005
Publicaciones de la RSME, vol. 10
Real Sociedad Matemática Española, Madrid, 2006
ISBN: 84-933610-7-0
J.F. Cariñena, X. Gràcia, G. Marmo, E. Martínez, M.-C. Muñoz-Lecanda and N. Román-Roy
"Geometric Hamilton-Jacobi theory"
Int. J. Geometric Methods in Mod. Phys. 3 (2006) 1417-1458
DOI: 10.1142/S0219887806001764 arXiv: math-ph/0604063
X. Gràcia and R. Martín
"Vector hulls and jet bundles", pp. 215-220 in
Proceedings of the XIII Fall Workshop on Geometry and Physics, Murcia, 2004
Publicaciones de la RSME, vol. 9
Real Sociedad Matemática Española, Madrid, 2005
ISBN: 84-933610-6-2
X. Gràcia and R. Martín
"Geometric aspects of time-dependent singular differential equations"
Int. J. Geometric Methods in Mod. Phys. 2 (2005) 597-618
DOI: 10.1142/S0219887805000697 abstract arXiv: math-ph/0410051
X. Gràcia and R. Martín
"Regularity and symmetries of nonholonomic systems"
J. Phys. A: Math. Gen. 38 (2005) 1071-1087
DOI: 10.1088/0305-4470/38/5/009 abstract arXiv: math-ph/0405066
X. Gràcia and R. Martín
"Time-dependent singular systems", pp. 155-160 in
Proceedings of the XII Fall Workshop on Geometry and Physics, Coimbra, 2003
edited by H. Albuquerque, R. Caseiro, J. Clemente-Gallardo, J.M. Nunes da Costa and J. Teles.
Publicaciones de la RSME, vol 7
Real Sociedad Matemática Española, Madrid, 2004
ISBN: 84-933610-3-8
X. Gràcia, M.-C. Muñoz-Lecanda and N. Román-Roy
"On some aspects of the geometry of differential equations in physics"
Int. J. Geometric Methods in Mod. Phys. 1 (2004) 265-284
DOI: 10.1142/S0219887804000150 abstract arXiv: math-ph/0402030
X. Gràcia and R. Martín
"Nonholonomic systems and the relativistic particle", pp. 223-228 in
Proceedings of the XI Fall Workshop on Geometry and Physics, Oviedo, 2002
edited by J. Fernández Núñez, W. García Fuertes and A. Viña Escalar
Publicaciones de la RSME, vol 6
Real Sociedad Matemática Española, Madrid, 2004
ISBN: 84-933610-1-1
X. Gràcia and J.M. Pons
"Symmetries of singular differential equations", pp. 159-168 in
Proceedings of the X Fall Workshop on Geometry and Physics, Miraflores de la Sierra, 2001
edited by A. González-López, M. Mañas, L. Martínez Alonso and M.Á. Rodríguez
Publicaciones de la RSME, vol 4
Real Sociedad Matemática Española, Madrid, 2003
ISBN: 84-923818-8-4
X. Gràcia, J. Marín-Solano and M.-C. Muñoz-Lecanda
"Some geometric aspects of variational calculus in constrained systems"
Rep. Math. Phys. 51 (2003) 127-148
DOI: 10.1016/S0034-4877(03)80006-X abstract arXiv: math-ph/0004019
X. Gràcia and J.M. Pons
"Symmetries and infinitesimal symmetries of singular differential equations"
J. Phys. A: Math. Gen. 35 (2002) 5059-5077
DOI: 10.1088/0305-4470/35/24/306 abstract arXiv: math-ph/0201034
X. Gràcia and J.M. Pons
"Some new geometric structures for singular lagrangians", pp. 227-232 in
Proceedings of the IX Fall Workshop on Geometry and Physics, Vilanova i la Geltrú, 2000
edited by X. Gràcia, J. Marín-Solano, M.-C. Muñoz-Lecanda and N. Román-Roy
Publicaciones de la RSME, vol. 3
Real Sociedad Matemática Española, Madrid, 2001
ISBN: 84-923818-5-X abstract compressed PS (62 KB).
X. Gràcia and J.M. Pons
"Singular lagrangians: some geometric structures along the Legendre map"
J. Phys. A: Math. Gen. 34 (2001) 3047-3070
DOI: 10.1088/0305-4470/34/14/311 abstract arXiv: math-ph/0009038
X. Gràcia and J.M. Pons
"Canonical Noether symmetries and commutativity properties for gauge systems"
J. Math. Phys. 41 (2000) 7333-7351
DOI: 10.1063/1.1289825 abstract arXiv: math-ph/0007037
X. Gràcia, J. Marín-Solano and M.-C. Muñoz-Lecanda
"Variational principles in mechanics: geometric aspects", pp. 81-94 in
Séptimo encuentro de otoño de geometría diferencial y sus aplicaciones,
edited by E. Llinares and J. Monterde.
Publicaciones de la RSME, vol. 1.
Real Sociedad Matemática Española, Madrid, 2000
ISBN: 84-923818-1-7 abstract compressed PS (1345 KB)
X. Gràcia
"Fibre derivatives: some applications to singular lagrangians"
Rep. Math. Phys. 45 (2000) 67-84
DOI: 10.1016/S0034-4877(00)88872-2 abstract arXiv: math-ph/0007038
X. Gràcia
"The fibre derivative and some of its applications", pp. 43-58 in
Proceedings of the V Fall Workshop: Geometry and Physics, 1996,
edited by J.F. Cariñena, E. Martínez and M.F. Rañada.
Memorias de la Real Academia de Ciencias Exactas, Físicas y Naturales de Madrid, serie de ciencias exactas, vol. 32
Real Academia de Ciencias Exactas, Físicas y Naturales, Madrid, 1998
ISBN: 84-87125-38-7 abstract
X. Gràcia and J.M. Pons
"Noether (and gauge) transformations for higher order singular lagrangians"
Proceedings of the Third Meeting on Current Ideas in Mechanics and Related Fields, Segovia (Spain), June 19-23, 1995
Extracta Mathematicae 11 (1996) 65-79
abstract
X. Gràcia, M.C. Muñoz-Lecanda and N. Román-Roy
"Singular systems: their origins, general features, and non numerical solution", pp. 31-36 in
IFAC Conference on System Structure and Control 1995, Nantes, France, 5-7 July 1995,
edited by M. Guglielmi.
IFAC Proceedings Volumes vol. 28 (8)
Elsevier, 1996
DOI: 10.1016/S1474-6670(17)45433-4 ISBN: 0-08-042356-6 abstract
X. Gràcia and J.M. Pons
"Gauge transformations for higher-order lagrangians"
J. Phys. A: Math. Gen. 28 (1995) 7181-7196
DOI: 10.1088/0305-4470/28/24/016 abstract arXiv: hep-th/9509094
X. Gràcia and J.M. Pons
"Noether transformations with vanishing conserved quantity"
Ann. Inst. H. Poicaré A 61 (1994) 315-327
NumDAM: AIHPA_1994__61_3_315_0 abstract
X. Gràcia, J.M. Pons and J. Roca
"Finite gauge transformations: the reparametrization algebras", pp. 21-27 in
Proceedings of the Fall Workshop on Differential Geometry and its Applications, Barcelona '93
edited by X. Gràcia, M.C. Muñoz and N. Román, 1994
ISBN 84-605-1284-3 abstract
X. Gràcia, J.M. Pons and J. Roca
"Closure of reparametrization algebras and flow-dependence of finite reparametrizations"
Int. J. Mod. Phys. A 9 (1994) 5001-5017
DOI: 10.1142/S0217751X94002016 abstract
X. Gràcia and J. Roca
"Covariant and noncovariant gauge transformations for the conformal particle"
Mod. Phys. Lett. A 8 (1993) 1747-1761
DOI: 10.1142/S0217732393001483 abstract
X. Gràcia and J.M. Pons
"A hamiltonian approach to lagrangian Noether transformations"
J. Phys. A: Math. Gen. 25 (1992) 6357-6369
DOI: 10.1088/0305-4470/25/23/029 abstract
X. Gràcia and J.M. Pons
"A generalized geometric framework for constrained systems"
Diff. Geom. Appl. 2 (1992) 223-247
DOI: 10.1016/0926-2245(92)90012-C abstract
X. Gràcia, J.M. Pons and N. Román-Roy
"Higher order conditions for singular lagrangian dynamics"
J. Phys. A: Math. Gen. 25 (1992) 1989-2004
DOI: 10.1088/0305-4470/25/7/037 abstract
X. Gràcia
Sistemes lligats: estudi geomètric i transformacions de simetria (in Catalan)
[Constrained systems: geometric study and symmetry transformations]
Ph.D. thesis, University of Barcelona, 1991.
Advisor: Josep M. Pons
ISBN 84-7875-790-2 abstract (English)
X. Gràcia, J.M. Pons and N. Román-Roy
"Higher order lagrangian systems: geometric structures, dynamics, and constraints"
J. Math. Phys. 32 (1991) 2744-2763
DOI: 10.1063/1.529066 abstract
X. Gràcia and J.M. Pons
"Constrained systems: a unified geometric approach"
Int. J. Theor. Phys. 30 (1991) 511-516
DOI: 10.1007/BF00672895 abstract
C. Batlle, J. Gomis, X. Gràcia and J.M. Pons
"Noether's theorem and gauge transformations: application to the bosonic string and CP₂^n-1 model"
J. Math. Phys. 30 (1989) 1345-1350
DOI: 10.1063/1.528598 abstract
X. Gràcia and J.M. Pons
"On an evolution operator connecting lagrangian and hamiltonian formalisms"
Lett. Math. Phys. 17 (1989) 175-180
DOI: 10.1007/BF00401582 abstract
X. Gràcia and J.M. Pons
"Gauge generators, Dirac's conjecture, and degrees of freedom for constrained systems"
Ann. Phys. (N.Y.) 187 (1988) 355-368
DOI: 10.1016/0003-4916(88)90153-4 abstract
X. Gràcia
Transformacions de gauge en sistemes dinàmics de dimensió finita (in Catalan)
[Gauge transformations in dynamical systems of finite dimension]
Tesina de llicenciatura (roughly equivalent to MSc thesis), University of Barcelona, 1987.
Advisor: Josep M. Pons
contents (English translation)

Publications as editor:

X. Gràcia, J. Marín-Solano, M.-C. Muñoz-Lecanda and N. Román-Roy (editors)
Proceedings of the IX Fall Workshop on Geometry and Physics, Vilanova i la Geltrú, 2000
Publicaciones de la RSME, vol. 3
Real Sociedad Matemática Española, Madrid, 2001

xii+270 pages ISBN: 84-923818-5-X
available also from the editors
Electronic version

X. Gràcia, M.C. Muñoz and N. Román (editors)
Proceedings of the Fall Workshop on Differential Geometry and its Applications, Barcelona '93
published in Barcelona by the editors, 1994

x+80 pages ISBN 84-605-1284-3
contents, preface, full text (PDF 849 KiB)

Back to Xavier Gràcia's home page

This web page: https://web.mat.upc.edu/xavier.gracia/xrecpubl.html. Last update: 2 July 2026.