Hamilton–Jacobi theory and integrability for autonomous and non-autonomous contact systems

[1]  Xavier Rivas,et al.  Nonautonomous k-contact field theories , 2022, Journal of Mathematical Physics.

[2]  M. Muñoz-Lecanda,et al.  Multicontact formulation for non-conservative field theories , 2022, Journal of Physics A: Mathematical and Theoretical.

[3]  X. Rivas,et al.  Lagrangian–Hamiltonian formalism for cocontact systems , 2023, Journal of Geometric Mechanics.

[4]  Jordi Gaset Rifà,et al.  Symmetries, conservation and dissipation in time-dependent contact systems , 2022, 2212.14848.

[5]  J. Grabowski,et al.  Contact geometric mechanics: the Tulczyjew triples , 2022, 2209.03154.

[6]  L. Colombo,et al.  Nonsmooth Herglotz variational principle , 2022, 2023 American Control Conference (ACC).

[7]  J. Lucas,et al.  Contact Lie systems: theory and applications , 2022, Journal of Physics A: Mathematical and Theoretical.

[8]  M. Muñoz-Lecanda,et al.  Time-dependent contact mechanics , 2022, Monatshefte für Mathematik.

[9]  M. Lainz,et al.  Discrete Hamilton–Jacobi theory for systems with external forces , 2021, Journal of Physics A: Mathematical and Theoretical.

[10]  Manuel Lainz,et al.  Geometric Hamilton–Jacobi theory for systems with external forces , 2021, Journal of Mathematical Physics.

[11]  N. Rom'an-Roy,et al.  Skinner–Rusk formalism for k-contact systems , 2021, Journal of Geometry and Physics.

[12]  M. D. Le'on,et al.  Optimal Control, Contact Dynamics and Herglotz Variational Problem , 2020, Journal of Nonlinear Science.

[13]  J. Grabowski,et al.  A novel approach to contact Hamiltonians and contact Hamilton-Jacobi theory , 2022 .

[14]  Manuel Lainz Valc'azar,et al.  Implicit contact dynamics and Hamilton-Jacobi theory , 2021, Differential Geometry and its Applications.

[15]  J. Marrero,et al.  Extended Hamilton–Jacobi Theory, Symmetries and Integrability by Quadratures , 2021, Mathematics.

[16]  M. de León,et al.  The Hamilton–Jacobi Theory for Contact Hamiltonian Systems , 2021, Mathematics.

[17]  S. Grillo Non-commutative integrability, exact solvability and the Hamilton–Jacobi theory , 2018, Analysis and Mathematical Physics.

[18]  M. D. Le'on,et al.  A review on contact Hamiltonian and Lagrangian systems , 2020, 2011.05579.

[19]  M. de León,et al.  Invariant measures for contact Hamiltonian systems: symplectic sandwiches with contact bread , 2020, Journal of Physics A: Mathematical and Theoretical.

[20]  A. Simoes,et al.  Contact geometry for simple thermodynamical systems with friction , 2020, Proceedings of the Royal Society A.

[21]  M. Muñoz-Lecanda,et al.  A K-contact Lagrangian formulation for nonconservative field theories , 2020, 2002.10458.

[22]  S. Grillo,et al.  Extended Hamilton–Jacobi theory, contact manifolds, and integrability by quadratures , 2019, Journal of Mathematical Physics.

[23]  Manuel Lainz Valc'azar,et al.  Infinitesimal symmetries in contact Hamiltonian systems , 2019, Journal of Geometry and Physics.

[24]  M. Muñoz-Lecanda,et al.  A contact geometry framework for field theories with dissipation , 2019, Annals of Physics.

[25]  M. D. Le'on,et al.  Hamilton–Jacobi theory for gauge field theories , 2019, 1904.10264.

[26]  S. Rashkovskiy Hamilton-Jacobi theory for Hamiltonian and non-Hamiltonian systems , 2017, Journal of Geometric Mechanics.

[27]  O. Esen,et al.  Hamilton–Jacobi formalism on locally conformally symplectic manifolds , 2019, Journal of Mathematical Physics.

[28]  Aritra Ghosh,et al.  Contact geometry and thermodynamics of black holes in AdS spacetimes , 2019, Physical Review D.

[29]  M. Muñoz-Lecanda,et al.  New contributions to the Hamiltonian and Lagrangian contact formalisms for dissipative mechanical systems and their symmetries , 2019, 1907.02947.

[30]  G. S. Frederico,et al.  Noether theorem for action-dependent Lagrangian functions: conservation laws for non-conservative systems , 2019, Nonlinear Dynamics.

[31]  Manuel Lainz Valc'azar,et al.  Singular Lagrangians and precontact Hamiltonian systems , 2019, International Journal of Geometric Methods in Modern Physics.

[32]  A. Bravetti Contact geometry and thermodynamics , 2019, International Journal of Geometric Methods in Modern Physics.

[33]  Manuel Lainz Valc'azar,et al.  Contact Hamiltonian systems , 2018, Journal of Mathematical Physics.

[34]  M. D. Le'on,et al.  A geometric Hamilton–Jacobi theory on a Nambu–Jacobi manifold , 2017, International Journal of Geometric Methods in Modern Physics.

[35]  Florio M. Ciaglia,et al.  Contact manifolds and dissipation, classical and quantum , 2018, Annals of Physics.

[36]  Chao Wang,et al.  Contact Hamiltonian dynamics: Variational principles, invariants, completeness and periodic behavior , 2018, Annals of Physics.

[37]  G. S. Frederico,et al.  An Action Principle for Action-dependent Lagrangians: toward an Action Principle to non-conservative systems , 2018, 1803.08308.

[38]  A. Schaft,et al.  Homogeneous Hamiltonian Control Systems Part I: Geometric Formulation , 2018 .

[39]  A. Schaft,et al.  Homogeneous Hamiltonian Control Systems Part II: Application to thermodynamic systems , 2018 .

[40]  F. Redig,et al.  A Hamilton-Jacobi point of view on mean-field Gibbs-non-Gibbs transitions , 2017, 1711.03489.

[41]  Florio M. Ciaglia,et al.  Hamilton-Jacobi Theory and Information Geometry , 2017, GSI.

[42]  Alessandro Bravetti,et al.  Contact Hamiltonian Dynamics: The Concept and Its Use , 2017, Entropy.

[43]  M. D. Le'on,et al.  A Hamilton-Jacobi theory for implicit differential systems , 2017, 1708.01586.

[44]  G. S. Frederico,et al.  Action principle for action-dependent Lagrangians toward nonconservative gravity: Accelerating universe without dark energy , 2017, 1705.04604.

[45]  M. de León,et al.  Cosymplectic and contact structures for time-dependent and dissipative Hamiltonian systems , 2016, 1612.06224.

[46]  M. León,et al.  Geometric Hamilton–Jacobi theory on Nambu–Poisson manifolds , 2016, 1604.08904.

[47]  Florio M. Ciaglia,et al.  Hamilton-Jacobi approach to Potential Functions in Information Geometry , 2016, 1608.06584.

[48]  A. Bravetti,et al.  Contact Hamiltonian Mechanics , 2016, 1604.08266.

[49]  S. Grillo,et al.  A Hamilton–Jacobi Theory for general dynamical systems and integrability by quadratures in symplectic and Poisson manifolds , 2015, 1512.03121.

[50]  Shin-itiro Goto,et al.  Contact geometric descriptions of vector fields on dually flat spaces and their applications in electric circuit models and nonequilibrium statistical mechanics , 2015, 1512.00950.

[51]  V. Zatloukal,et al.  Classical field theories from Hamiltonian constraint: Canonical equations of motion and local Hamilton-Jacobi theory , 2015, 1504.08344.

[52]  D. D. Diego,et al.  Hamilton-Jacobi theory in Cauchy data space , 2014, 1411.3959.

[53]  D. D. Diego,et al.  A Hamilton-Jacobi theory on Poisson manifolds , 2014 .

[54]  M. D. Le'on,et al.  Geometric Hamilton–Jacobi theory for higher-order autonomous systems , 2013, 1309.2166.

[55]  A. Kholodenko Applications Of Contact Geometry And Topology In Physics , 2013 .

[56]  M. D. Le'on,et al.  Hamilton-Jacobi theory in k-cosymplectic field theories , 2013, 1304.3360.

[57]  M. Leok,et al.  Dirac Structures and Hamilton-Jacobi Theory for Lagrangian Mechanics on Lie Algebroids , 2012, 1211.4561.

[58]  A. Budiyono Quantization from Hamilton–Jacobi theory with a random constraint , 2012, 1205.0244.

[59]  D. D. Diego,et al.  A Hamilton-Jacobi Theory for Singular Lagrangian Systems in the Skinner and Rusk Setting , 2012, 1205.0168.

[60]  D. D. Diego,et al.  On the Hamilton-Jacobi Theory for Singular Lagrangian Systems , 2012, 1204.6217.

[61]  L. Vitagliano GEOMETRIC HAMILTON–JACOBI FIELD THEORY , 2011, 1109.1677.

[62]  Tomoki Ohsawa,et al.  Hamilton-Jacobi Theory for Degenerate Lagrangian Systems with Holonomic and Nonholonomic Constraints , 2011, 1109.6056.

[63]  A. Bloch,et al.  Nonholonomic Hamilton-Jacobi theory via Chaplygin Hamiltonization , 2011, 1102.4361.

[64]  C. Boyer Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on S^2×S^3 , 2011, 1101.5587.

[65]  G. Marmo,et al.  Geometric Hamilton-Jacobi theory for nonholonomic dynamical systems , 2009, 0908.2453.

[66]  S. Tabachnikov,et al.  Contact complete integrability , 2009, 0910.0375.

[67]  N. Mukunda,et al.  The Hamilton--Jacobi Theory and the Analogy between Classical and Quantum Mechanics , 2009, 0907.0964.

[68]  G. Marmo,et al.  Hamilton-Jacobi theory and the evolution operator , 2009, 0907.1039.

[69]  Juan Carlos Marrero,et al.  Linear almost Poisson structures and Hamilton-Jacobi equation. Applications to nonholonomic Mechanics , 2008, 0801.4358.

[70]  Hansjörg Geiges,et al.  An introduction to contact topology , 2008 .

[71]  M. León,et al.  Towards a Hamilton–Jacobi theory for nonholonomic mechanical systems , 2007, 0705.3739.

[72]  G. Marmo,et al.  Geometric Hamilton-Jacobi theory , 2006, math-ph/0604063.

[73]  M. Montesinos,et al.  Hamilton-Jacobi theory for Hamiltonian systems with non-canonical symplectic structures , 2006, gr-qc/0601140.

[74]  Noboru Sakamoto,et al.  Analysis of the Hamilton--Jacobi Equation in Nonlinear Control Theory by Symplectic Geometry , 2001, SIAM J. Control. Optim..

[75]  M. León,et al.  Gradient vector fields on cosymplectic manifolds , 1992 .

[76]  Charles-Michel Marle,et al.  Symplectic geometry and analytical mechanics , 1987 .

[77]  V. Arnold Mathematical Methods of Classical Mechanics , 1974 .

[78]  P J Fox,et al.  THE FOUNDATIONS OF MECHANICS. , 1918, Science.