- Previous Article
- JGM Home
- This Issue
-
Next Article
Bundle-theoretic methods for higher-order variational calculus
A Hamilton-Jacobi theory on Poisson manifolds
1. | Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), c\ Nicolás Cabrera, n 13-15, Campus Cantoblanco, UAM, 28049 Madrid, Spain, Spain, Spain |
References:
[1] |
2nd ed., Benjamin-Cummings, Reading (Ma), 1978. |
[2] |
Second edition. Graduate Texts in Mathematics, 60. Springer-Verlag, New York, 1989. |
[3] |
Nonlinearity, 23 (2010), 1887-1918.
doi: 10.1088/0951-7715/23/8/006. |
[4] |
Rep. Math. Phys., 32 (1993), 99-115.
doi: 10.1016/0034-4877(93)90073-N. |
[5] |
J. Math. Phys., 23 (1982), 1589-1595.
doi: 10.1063/1.525569. |
[6] |
Nonlinearity, 12 (1999), 721-737.
doi: 10.1088/0951-7715/12/3/316. |
[7] |
Int. J. Geom. Meth. Mod. Phys., 3 (2006), 1417-1458.
doi: 10.1142/S0219887806001764. |
[8] |
Int. J. Geom. Meth. Mod. Phys., 7 (2010), 431-454.
doi: 10.1142/S0219887810004385. |
[9] |
Hermann, Paris, 1969. |
[10] |
Journal of Mathematical Physics, 53 (2012), 072905 (29 pages).
doi: 10.1063/1.4736733. |
[11] |
Journal of Physics A: Math. Gen., 41 (2008), 015205, 14 pp.
doi: 10.1088/1751-8113/41/1/015205. |
[12] |
In: Variations, geometry and physics, 129-140, Nova Sci. Publ., New York, (2009). |
[13] |
J. Geom. Mech., 2 (2010), 159-198.
doi: 10.3934/jgm.2010.2.159. |
[14] |
Int. J. Geom. Meth. Mod. Phys., 7 (2010), 1491-1507.
doi: 10.1142/S0219887810004919. |
[15] |
J. Math. Phys., 54 (2013), 032902, 32 pp.
doi: 10.1063/1.4796088. |
[16] |
Int. J. Geom. Meth. Mod. Phys., 9 (2012), 1250074, 24 pp.
doi: 10.1142/S0219887812500740. |
[17] |
M. de León, D. Martín de Diego, C. Martínez-Campos and M. Vaquero, A Hamilton-Jacobi theory in infinite dimensional phase spaces,, In preparation., (). Google Scholar |
[18] |
North-Holland Mathematics Studies, 158. North-Holland Publishing Co., Amsterdam, 1989. |
[19] |
D. Reidel Publishing Co., Dordrecht, 1987.
doi: 10.1007/978-94-009-3807-6. |
[20] |
Int. J. Geom. Methods Mod. Phys., 3 (2006), 605-622.
doi: 10.1142/S0219887806001284. |
[21] |
J. Geom. Mech., 1 (2009), 461-481.
doi: 10.3934/jgm.2009.1.461. |
[22] |
Hazell, Watson and Viney Ltd., Aylesbury, Buckinghamshire, U.K. 1966. Google Scholar |
[23] |
Progress in Mathematics, 118. Birkhäuser Verlag, Basel, 1994.
doi: 10.1007/978-3-0348-8495-2. |
[24] |
Rep. Math. Phys., 34 (1994), 225-233.
doi: 10.1016/0034-4877(94)90038-8. |
show all references
References:
[1] |
2nd ed., Benjamin-Cummings, Reading (Ma), 1978. |
[2] |
Second edition. Graduate Texts in Mathematics, 60. Springer-Verlag, New York, 1989. |
[3] |
Nonlinearity, 23 (2010), 1887-1918.
doi: 10.1088/0951-7715/23/8/006. |
[4] |
Rep. Math. Phys., 32 (1993), 99-115.
doi: 10.1016/0034-4877(93)90073-N. |
[5] |
J. Math. Phys., 23 (1982), 1589-1595.
doi: 10.1063/1.525569. |
[6] |
Nonlinearity, 12 (1999), 721-737.
doi: 10.1088/0951-7715/12/3/316. |
[7] |
Int. J. Geom. Meth. Mod. Phys., 3 (2006), 1417-1458.
doi: 10.1142/S0219887806001764. |
[8] |
Int. J. Geom. Meth. Mod. Phys., 7 (2010), 431-454.
doi: 10.1142/S0219887810004385. |
[9] |
Hermann, Paris, 1969. |
[10] |
Journal of Mathematical Physics, 53 (2012), 072905 (29 pages).
doi: 10.1063/1.4736733. |
[11] |
Journal of Physics A: Math. Gen., 41 (2008), 015205, 14 pp.
doi: 10.1088/1751-8113/41/1/015205. |
[12] |
In: Variations, geometry and physics, 129-140, Nova Sci. Publ., New York, (2009). |
[13] |
J. Geom. Mech., 2 (2010), 159-198.
doi: 10.3934/jgm.2010.2.159. |
[14] |
Int. J. Geom. Meth. Mod. Phys., 7 (2010), 1491-1507.
doi: 10.1142/S0219887810004919. |
[15] |
J. Math. Phys., 54 (2013), 032902, 32 pp.
doi: 10.1063/1.4796088. |
[16] |
Int. J. Geom. Meth. Mod. Phys., 9 (2012), 1250074, 24 pp.
doi: 10.1142/S0219887812500740. |
[17] |
M. de León, D. Martín de Diego, C. Martínez-Campos and M. Vaquero, A Hamilton-Jacobi theory in infinite dimensional phase spaces,, In preparation., (). Google Scholar |
[18] |
North-Holland Mathematics Studies, 158. North-Holland Publishing Co., Amsterdam, 1989. |
[19] |
D. Reidel Publishing Co., Dordrecht, 1987.
doi: 10.1007/978-94-009-3807-6. |
[20] |
Int. J. Geom. Methods Mod. Phys., 3 (2006), 605-622.
doi: 10.1142/S0219887806001284. |
[21] |
J. Geom. Mech., 1 (2009), 461-481.
doi: 10.3934/jgm.2009.1.461. |
[22] |
Hazell, Watson and Viney Ltd., Aylesbury, Buckinghamshire, U.K. 1966. Google Scholar |
[23] |
Progress in Mathematics, 118. Birkhäuser Verlag, Basel, 1994.
doi: 10.1007/978-3-0348-8495-2. |
[24] |
Rep. Math. Phys., 34 (1994), 225-233.
doi: 10.1016/0034-4877(94)90038-8. |
[1] |
Olivier Ley, Erwin Topp, Miguel Yangari. Some results for the large time behavior of Hamilton-Jacobi equations with Caputo time derivative. Discrete & Continuous Dynamical Systems, 2021, 41 (8) : 3555-3577. doi: 10.3934/dcds.2021007 |
[2] |
Qiwei Wu, Liping Luan. Large-time behavior of solutions to unipolar Euler-Poisson equations with time-dependent damping. Communications on Pure & Applied Analysis, 2021, 20 (3) : 995-1023. doi: 10.3934/cpaa.2021003 |
[3] |
Ahmad El Hajj, Hassan Ibrahim, Vivian Rizik. $ BV $ solution for a non-linear Hamilton-Jacobi system. Discrete & Continuous Dynamical Systems, 2021, 41 (7) : 3273-3293. doi: 10.3934/dcds.2020405 |
[4] |
Paul Deuring. Spatial asymptotics of mild solutions to the time-dependent Oseen system. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021044 |
[5] |
Ying Sui, Huimin Yu. Singularity formation for compressible Euler equations with time-dependent damping. Discrete & Continuous Dynamical Systems, 2021 doi: 10.3934/dcds.2021062 |
[6] |
Elena K. Kostousova. External polyhedral estimates of reachable sets of discrete-time systems with integral bounds on additive terms. Mathematical Control & Related Fields, 2021 doi: 10.3934/mcrf.2021015 |
[7] |
Yueqiang Shang, Qihui Zhang. A subgrid stabilizing postprocessed mixed finite element method for the time-dependent Navier-Stokes equations. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3119-3142. doi: 10.3934/dcdsb.2020222 |
[8] |
Masahiro Ikeda, Ziheng Tu, Kyouhei Wakasa. Small data blow-up of semi-linear wave equation with scattering dissipation and time-dependent mass. Evolution Equations & Control Theory, 2021 doi: 10.3934/eect.2021011 |
[9] |
Michiyuki Watanabe. Inverse $N$-body scattering with the time-dependent hartree-fock approximation. Inverse Problems & Imaging, 2021, 15 (3) : 499-517. doi: 10.3934/ipi.2021002 |
[10] |
Manuel de León, Víctor M. Jiménez, Manuel Lainz. Contact Hamiltonian and Lagrangian systems with nonholonomic constraints. Journal of Geometric Mechanics, 2021, 13 (1) : 25-53. doi: 10.3934/jgm.2021001 |
[11] |
Felix Finster, Jürg Fröhlich, Marco Oppio, Claudio F. Paganini. Causal fermion systems and the ETH approach to quantum theory. Discrete & Continuous Dynamical Systems - S, 2021, 14 (5) : 1717-1746. doi: 10.3934/dcdss.2020451 |
[12] |
F.J. Herranz, J. de Lucas, C. Sardón. Jacobi--Lie systems: Fundamentals and low-dimensional classification. Conference Publications, 2015, 2015 (special) : 605-614. doi: 10.3934/proc.2015.0605 |
[13] |
Daniele Cassani, Luca Vilasi, Jianjun Zhang. Concentration phenomena at saddle points of potential for Schrödinger-Poisson systems. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021039 |
[14] |
Yuri Fedorov, Božidar Jovanović. Continuous and discrete Neumann systems on Stiefel varieties as matrix generalizations of the Jacobi–Mumford systems. Discrete & Continuous Dynamical Systems, 2021, 41 (6) : 2559-2599. doi: 10.3934/dcds.2020375 |
[15] |
John Leventides, Costas Poulios, Georgios Alkis Tsiatsios, Maria Livada, Stavros Tsipras, Konstantinos Lefcaditis, Panagiota Sargenti, Aleka Sargenti. Systems theory and analysis of the implementation of non pharmaceutical policies for the mitigation of the COVID-19 pandemic. Journal of Dynamics & Games, 2021 doi: 10.3934/jdg.2021004 |
[16] |
Beom-Seok Han, Kyeong-Hun Kim, Daehan Park. A weighted Sobolev space theory for the diffusion-wave equations with time-fractional derivatives on $ C^{1} $ domains. Discrete & Continuous Dynamical Systems, 2021, 41 (7) : 3415-3445. doi: 10.3934/dcds.2021002 |
[17] |
Fangyi Qin, Jun Wang, Jing Yang. Infinitely many positive solutions for Schrödinger-poisson systems with nonsymmetry potentials. Discrete & Continuous Dynamical Systems, 2021 doi: 10.3934/dcds.2021054 |
[18] |
Wei-Jian Bo, Guo Lin, Shigui Ruan. Traveling wave solutions for time periodic reaction-diffusion systems. Discrete & Continuous Dynamical Systems, 2018, 38 (9) : 4329-4351. doi: 10.3934/dcds.2018189 |
[19] |
Elimhan N. Mahmudov. Second order discrete time-varying and time-invariant linear continuous systems and Kalman type conditions. Numerical Algebra, Control & Optimization, 2021 doi: 10.3934/naco.2021010 |
[20] |
Quan Hai, Shutang Liu. Mean-square delay-distribution-dependent exponential synchronization of chaotic neural networks with mixed random time-varying delays and restricted disturbances. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3097-3118. doi: 10.3934/dcdsb.2020221 |
2019 Impact Factor: 0.649
Tools
Metrics
Other articles
by authors
[Back to Top]