Related papers: Local Physical Coodinates from Symplectic Projecto…

Obtaining complete information about the shape of an object by looking at it from a single direction is impossible in general. In this paper, we theoretically study obtaining differential geometric information of an object from orthogonal…

We have reported previously on a new method we are developing for using image-based information to improve global coronal magnetic field models. In that work we presented early tests of the method which proved its capability to improve…

We propose a visualization method to understand the effect of multidimensional projection on local subspaces, using implicit function differentiation. Here, we understand the local subspace as the multidimensional local neighborhood of data…

In this text, we explore the tools that Projective Differential Geometry can provide for the asymptotic analysis of classical fields on projectively compact manifolds. We emphasise on the case of order 2-compactifications and develop, in…

We present a new automated method for finding integrable symplectic maps of the plane. These dynamical systems possess a hidden symmetry associated with an existence of conserved quantities, i.e. integrals of motion. The core idea of the…

In this note we give simple symplecticity conditions for implicit schemes in the linear case. We consider implicit maps on generic symplectic manifold and we introduce the concept of consistent implicit maps, to generalize the symplecticity…

Retraction maps have been generalized to discretization maps in (Barbero Li\~n\'an and and Mart\'{\i}n de Diego, 2022). Discretization maps are used to systematically derive numerical integrators that preserve the symplectic structure, as…

Classical energy-momentum methods study the existence and stability properties of solutions of $t$-dependent Hamilton equations on symplectic manifolds whose evolution is given by their Hamiltonian Lie symmetries. The points of such…

In this paper we derive the symplectic framework for field theories defined by higher-order Lagrangians. The construction is based on the symplectic reduction of suitable spaces of iterated jets. The possibility of reducing a higher-order…

The tools of presymplectic geometry are used to study light rays trajectories in anisotropic media.

We review recent results and ongoing investigations of the symplectic and Poisson geometry of derived moduli spaces, and describe applications to deformation quantization of such spaces.

In this paper we provide a complete characterisation of coisotropic embeddings of precosymplectic manifolds into cosymplectic manifolds. This result extends a theorem of Gotay about coisotropic embeddings of presymplectic manifolds. We also…

We consider a generalization of the notion of a natural mechanical system to the case of additional forces of gyroscopic type. Such forces appear, for example, as a result of global reduction of a natural system with symmetry. We study…

Log-symplectic structures are Poisson structures that are determined by a symplectic form with logarithmic singularities. We construct moduli spaces of curves with values in a log-symplectic manifold. Among the applications, we classify…

We study neighborhoods of configurations of symplectic surfaces in symplectic 4-manifolds. We show that suitably `positive' configurations have neighborhoods with concave boundaries and we explicitly describe open book decompositions of the…

This paper discusses the construction of local bounded commuting projections for discrete subcomplexes of the gradgrad complexes in two and three dimensions, which play an important role in the finite element theory of elasticity (2D) and…

This is a survey written in an expositional style on the topic of symplectic singularities and symplectic resolutions, which could also serve as an introduction to this subject.

We define the concept of symplectic foliation on a symplectic manifold and provide a method of constructing many examples, by using asymptotically holomorphic techniques.

Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…

We develop efficient and high-order accurate finite difference methods for elliptic partial differential equations in complex geometry in the Difference Potentials framework. The main novelty of the developed schemes is the use of local…