Related papers: Discrete Dynamics on Locally Conformal Framework
Models involving hybrid systems are versatile in their application but difficult to optimize efficiently due to their combinatorial nature. This work presents a method to cope with hybrid optimal control problems which, in contrast to…
The generic behavior of purely dissipative open quantum many-body systems with local dissipation processes can be investigated using random matrix theory, revealing a hierarchy of decay timescales of observables organized by their…
The SL(2,R) invariant Hamiltonian systems are discussed within the frame- work of the orbit method. It is shown that both dynamics and symmetry trans- formations are globally well-defined on phase space. The flexibility in the choice of…
We introduce a version of the Hamiltonian formalism based on the Clairaut equation theory, which allows us a self-consistent description of systems with degenerate (or singular) Lagrangian. A generalization of the Legendre transform to the…
This article is concerned with analytic Hamiltonian dynamical systems in infinite dimension in a neighborhood of an elliptic fixed point. Given a quadratic Hamiltonian, we consider the set of its analytic higher order perturbations. We…
The global time is defined in covariant form under the condition of a constant mean curvature slicing of spacetime. The background static metric is taken in the tangent space. The global intrinsic time is identified with the logarithmic…
We examine "dynamical similarities" in the Lagrangian framework. These are symmetries of an intrinsically determined physical system under which observables remain unaffected, but the extraneous information is changed. We establish three…
Many integrable hierarchies of differential equations allow a variational description, called a Lagrangian multiform or a pluri-Lagrangian structure. The fundamental object in this theory is not a Lagrange function but a differential…
In this paper we present a general framework that allows one to study discretization of certain dynamical systems. This generalizes earlier work on discretization of Lagrangian and Hamiltonian systems on tangent bundles and cotangent…
In this article we present a Lagrangian representation for evolutionary systems with a Hamiltonian structure determined by a differential-geometric Poisson bracket of the first order associated with metrics of constant curvature.…
We apply the Dirac procedure for constrained systems to the Arnowitt-Deser-Misner formalism linearized around the Friedmann-Lemaitre universe. We explain and employ some basic concepts such as Dirac observables, Dirac brackets, gauge-fixing…
I review the classical and quantum dynamics of systems with local world-line supersymmetry. The hamiltonian formulation, in particular the covariant hamiltonian approach, is emphasized. Anomalous behaviour of local quantum supersymmetry is…
This paper introduces a new global dynamics and chaos indicator based on the method of Lagrangian Descriptor apt for discriminating ordered and deterministic chaotic motions in multidimensional systems. The selected implementation of this…
We present some relaxation and integral representation results for energy functionals in the setting of structured deformations, with special emphasis given to the case of multi-level structured deformations. In particular, we present an…
We develop Hamiltonian formalism for Lagrange Multiplier Modified Gravity. We further calculate the Poisson brackets between constraints and we show that they coincide with the algebra of constraints in Hamiltonian formulation of General…
We consider the relativistic generalization of the harmonic oscillator problem by addressing different questions regarding its classical aspects. We treat the problem using the formalism of Hamiltonian mechanics. A Lie algebraic technique…
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of…
The geometric framework for the Hamilton-Jacobi theory is used to study this theory in the ambient of higher-order mechanical systems, both in the Lagrangian and Hamiltonian formalisms. Thus, we state the corresponding Hamilton-Jacobi…
A variational framework for accelerated optimization was recently introduced on normed vector spaces and Riemannian manifolds in Wibisono et al. (2016) and Duruisseaux and Leok (2021). It was observed that a careful combination of…
The present work investigates the evolution of linear perturbations of time-dependent ideal fluid flows with advected quantities, expressed in terms of the second order variations of the action corresponding to a Lagrangian defined on a…