Related papers: A note on the representability of a certain Hamilt…

While the Hamiltonian group actions on closed symplectic manifolds have been widely explored throughout the last couple of decades, the study on Hamiltonian group actions on symplectic manifolds with a contact type boundary has started only…

We consider the Hamiltonian for a charged particle in a harmonic potential in the presence of a magnetic field. The most symmetric case depends on one parameter, the variation of which leads from a spectrum bounded from below to an…

We present a definition of generating functions of canonical relations, which are real functions on symmetric symplectic spaces, discussing some conditions for the presence of caustics. We show how the actions compose by a neat geometrical…

Hamiltonian quantization of an integral compact symplectic manifold M depends on a choice of compatible almost complex structure J. For open sets U in the set of compatible almost complex structures and small enough values of Planck's…

The contact geometric structure of the thermodynamic phase space is used to introduce a novel symplectic structure on the tangent bundle of the equilibrium space. Moreover, it turns out that the equilibrium space can be interpreted as a…

We give a comparative description of the Poisson structures on the moduli spaces of flat connections on real surfaces and holomorphic Poisson structures on the moduli spaces of holomorphic bundles on complex surfaces. The symplectic leaves…

In this paper we present a unifying geometric and compositional framework for modeling complex physical network dynamics as port-Hamiltonian systems on open graphs. Basic idea is to associate with the incidence matrix of the graph a Dirac…

Let L->M be a Hermitian line bundle over a compact manifold. Write S for the space of all unitary connections in L whose curvatures define symplectic forms on M and G for the group of unitary bundle isometries of L, which acts on S by…

Singular theories, characterised by the presence of degeneracies in their Lagrangian or Hamiltonian descriptions, require the systematic implementation of constraints in order to obtain well-defined dynamics. While the symplectic framework…

We derived a condition under which a coupled system consisting of two finite-dimensional Hamiltonian systems becomes a Hamiltonian system. In many cases, an industrial system can be modeled as a coupled system of some subsystems. Although…

Inductive bias refers to restrictions on the hypothesis class that enable a learning method to generalize effectively from limited data. A canonical example in control is linearity, which underpins low sample-complexity guarantees for…

We study the symplectic semi-characteristic of a closed 4n-dimensional symplectic manifold. First, using the even-degree part of the primitive cohomology, we define the symplectic semi-characteristic. Second, using a vector field with…

Integrable Hamiltonian systems on symplectic manifolds have been well-studied. However, an intrinsic property of these kind of systems is that they can only live on even dimensional manifolds. To introduce a similar notion of integrability…

We give insight in the structure of port-Hamiltonian systems as control systems in between two closed Hamiltonian systems. Using the language of category theory, we identify systems with their behavioural representation and view a…

Let X be a four-manifold with boundary three manifold M. We shall describe (i) a pre-symplectic structure on the space of connections of the trivial SU(n)-bundle over X that comes from the canonical symplectic structure on the cotangent…

The aim of this paper is to develop a Hamilton--Jacobi theory for contact Hamiltonian systems. We find several forms for a suitable Hamilton-Jacobi equation accordingly to the Hamiltonian and the evolution vector fields for a given…

Many of the existing results for closed Hamiltonian G-manifolds are based on the analysis of the corresponding Hamiltonian functions using Morse-Bott techniques. In general such methods fail for non-compact manifolds or for manifolds with…

We address the breakdown of the bulk-boundary correspondence observed in non-Hermitian systems, where open and periodic systems can have distinct phase diagrams. The correspondence can be completely restored by considering the Hamiltonian's…

We prove that the Floer complex that is associated with a convex Hamiltonian function on $\mathbb{R}^{2n}$ is isomorphic to the Morse complex of Clarke's dual action functional that is associated with the Fenchel-dual Hamiltonian. This…

Motivated by relations with a symplectic invariant known as the "cylindrical symplectic capacity", in this note we study the expectation of the area of a minimal projection to a complex line for a randomly rotated cube.