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

@inproceedings{Leon2022HamiltonJacobiTA, title={Hamilton-Jacobi theory and integrability for autonomous and non-autonomous contact systems}, author={Manuel de Le'on and Manuel Lainz and Asier L'opez-Gord'on and Xavier Rivas}, year={2022} }

In this paper, we study the integrability of contact Hamiltonian systems, both time-dependent and independent. In order to do so, we construct a Hamilton–Jacobi theory for these systems following two approaches, obtaining two diﬀerent Hamilton–Jacobi equations. Compared to conservative Hamiltonian systems, contact Hamiltonian systems depend of one additional parameter. The fact of obtaining two equations reﬂects whether we are looking for solutions depending on this additional parameter or not…

## 3 Citations

### Geometric Hamilton-Jacobi theory and integrability for nonholonomic and forced hybrid systems

- Mathematics
- 2022

. A hybrid system is a system whose dynamics are controlled by a mixture of both continuous and discrete transitions. The geometric framework for the Hamilton–Jacobi theory is developed to study this…

### Symmetries, conservation and dissipation in time-dependent contact systems

- Mathematics
- 2022

In contact Hamiltonian systems, the so-called dissipated quantities are akin to conserved quantities in classical Hamiltonian systems. In this paper, we prove a Noether’s theorem for non-autonomous…

### Multicontact formulation for non-conservative field theories

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2023

A new geometric framework is developed to describe non-conservative classical field theories, which is based on multisymplectic and contact geometries. Assuming certain additional conditions and…

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