2 citations · 2 across the 8 of their papers we have counts for
11 papers · 1 filter
Dirac Structures and Reduction of Optimal Control Problems with Symmetries
A. Ibort, M. Leok, R. Salmoni +1
We study the symmetry reduction of optimal control problems using Dirac structures. The first-order conditions of the Pontryagin Maximum Principle are written as an implicit Dirac…
A Morse-Family Integrator for Hamilton--Jacobi Dynamics Across Caustics
F. Jiménez Alburquerque, M. Leok, C. Sardón +1
We develop a geometric framework for implicit discrete Hamiltonian systems based on discrete Morse families, Lagrangian relations, and discrete analogues of Tulczyjew's triple. The…
Hamilton--Jacobi theory for non-conservative field theories in the -contact framework
Javier de Lucas, Julia Lange, Xavier Rivas +1
This article develops a Hamilton--Jacobi theory for non-conservative classical field theories, with particular emphasis on dissipative systems, in the framework of co-oriented k-co…
Noether-Type Theorems and the Generalized Herglotz Principle in -Contact Geometry
Melvin Leok, Cristina Sardón, Xuefeng Zhao
We develop a unified geometric framework for dissipative mechanical systems based on uniform -contact manifolds, which provide an extended phase space equipped with multiple con…
Exact integration of Hamiltonian dynamics via Jacobi and Poisson Cinf-structures
A. J. Pan-Collantes, C. Sardón, X. Zhao
We develop a geometric framework for the exact integration of Hamiltonian systems based on triangular closure relations among a finite family of functions. Unlike Liouville-Arnold…
Symmetries and Weighted Integrability of Vector Fields with Jacobi Multipliers
C. Sardón, X. Zhao
In this paper, we investigate analytic divergence-free vector fields and vector fields admitting a Jacobi multiplier on -dimensional Riemannian manifolds. We first introduce a f…
(Quasi) Hamiltonian Systems and Non-Decomposable Poisson Geometry
C. Sardón, X. Zhao
In this work, we conduct a systematic study of Hamiltonian and quasi-Hamiltonian systems within the framework of nondecomposable generalized Poisson geometry. Our focus lies on the…
From Dirac to Dunkl Operators through Symmetry Reduction
Cristina Sardón
This paper presents a geometric and analytic derivation of Dirac-Dunkl operators as symmetry reductions of the flat Dirac operator on Euclidean space. Starting from the standard Di…
Integration on -Cosymplectic Manifolds
M. Leok, C. Sardón, X. Zhao
This paper presents a unified framework for studying dynamics and integration on -cosymplectic manifolds. After outlining the geometric foundations of -cosymplectic structure…
q-Cosymplectic Geometry, Integrability and Reduction
Melvin Leok, Cristina Sardón, Xuefeng Zhao
In the present paper, we define the concept of a \( q \)-cosymplectic manifold, on which we study the Hamiltonian, gradient, local gradient, and \( q \)-evolution vector fields. Se…
Non-isospectral 1+1 hierarchies arising from a Camassa--Holm hierarchy in 2+1 dimensions
P. G. Estévez, C. Sardón
The non-isospectral problem (Lax pair) associated with a hierarchy in 2+1 dimensions that generalizes the well known Camassa-Holm hierarchy is presented. Here, we have investigated…