Related papers: Circle complexes and the discrete CKP equation
A class of discrete equations is considered from three perspectives corresponding to three measures of the complexity of solutions: the (hyper-) order of meromorphic solutions in the sense of Nevanlinna, the degree growth of iterates over a…
This thesis is a study of large sets of unit vectors in $\cx^n$ such that the absolute value of their standard inner products takes on only a small number of values. We begin with bounds: what is the maximal size of a set of lines with only…
KdV6 equation can be described as the Kupershmidt deformation of the KdV equation (see 2008, Phys. Lett. A 372: 263). In this paper, starting from the bi-Hamiltonian structure of the discrete integrable system, we propose a generalized…
In this paper, we continue the construction of variational integrators adapted to contact geometry started in \cite{VBS}, in particular, we introduce a discrete Herglotz Principle and the corresponding discrete Herglotz Equations for a…
A novel class of discrete integrable surfaces is recorded. This class of discrete O surfaces is shown to include discrete analogues of classical surfaces such as isothermic, `linear' Weingarten, Guichard and Petot surfaces. Moreover,…
The differential system for minimal Lagrangian surfaces in a $2_{\mathbb{C}}$-dimensional, non-flat, complex space form is an elliptic system defined on the bundle of oriented Lagrangian planes. This is a 6-symmetric space associated with…
A Lie algebra structure on variation vector fields along an immersed curve in a $2$-dimensional real space form is investigated. This Lie algebra particularized to plane curves is the cornerstone in order to define a Hamiltonian structure…
In this paper, a new higher Hochschild Complex is defined with an Iterated Integral map to locally model differential forms on the space of bigons on $M$. In particular, given the local data for a gerbe with structure 2-group given by a…
We prove that the homology classes of closed geodesics associated to subgroups of narrow class groups of real quadratic fields concentrate around the Eisenstein line. This fits into the framework of Duke's Theorem and can be seen as a real…
We study the projective systems in both continuous and discrete settings. These systems are linearizable by construction and thus, obviously, integrable. We show that in the continuous case it is possible to eliminate all variables but one…
Solutions to vacuum Einstein field equations with cosmological constant, such as the de Sitter space and the anti-de Sitter space, are basic in different cosmological and theoretical developments. It is also well known that complex…
A general scheme for determining and studying integrable deformations of algebraic curves is presented. The method is illustrated with the analysis of the hyperelliptic case. An associated multi-Hamiltonian hierarchy of systems of…
Nineteen classical superintegrable systems in two-dimensional non-Euclidean spaces are shown to possess hidden symmetries leading to their linearization. They are the two Perlick systems [A. Ballesteros, A. Enciso, F.J. Herranz and O.…
Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…
In many applications, one encounters signals that lie on manifolds rather than a Euclidean space. In particular, covariance matrices are examples of ubiquitous mathematical objects that have a non Euclidean structure. The application of…
Various simplicial complexes can be associated with a graph. Box complexes form an important families of such simplicial complexes and are especially useful for providing lower bounds on the chromatic number of the graph via some of their…
We prove that many aspects of the differential geometry of embedded Riemannian manifolds can be formulated in terms of multi linear algebraic structures on the space of smooth functions. In particular, we find algebraic expressions for…
We show that various classical theorems of real/complex linear incidence geometry, such as the theorems of Pappus, Desargues, M\"obius, and so on, can be interpreted as special cases of a single "master theorem" that involves an arbitrary…
We prove that the set of non-degenerate second order maximally superintegrable systems in the complex Euclidean plane carries a natural structure of a projective variety, equipped with a linear isometry group action. This is done by…
The system of $N$ classical particles on the line with the Weierstrass $\wp$ function as potential is known to be completely integrable. Recently D'Hoker and Phong found a beautiful parameterization by the polynomial of degree $N$ of the…