Related papers: Two-dimensional Systems that Arise from the Noethe…

We tersely review a recently introduced technique to identify systems of two nonlinearly-coupled Ordinary Di{\S}erential Equations (ODEs) solvable by algebraic operations; and we report some specifc examples of this kind, namely systems of…

We study differential systems for which it is possible to establish a correspondence between symmetries and conservation laws based on Noether identity: quasi-Noether systems. We analyze Noether identity and show that it leads to the same…

In this set of papers we formulate a stand alone method to derive maximal number of linearizing transformations for nonlinear ordinary differential equations (ODEs) of any order including coupled ones from a knowledge of fewer number of…

Here we consider scale invariant dynamical systems within a classical particle description of Lagrangian mechanics. We begin by showing the condition under which a spatial and temporal scale transformation of such a system can lead to a…

The existence of a Lagrangian description for the second-order Riccati equation is analyzed and the results are applied to the study of two different nonlinear systems both related with the generalized Riccati equation. The Lagrangians are…

We exploit the key idea that nonlinear system identification is equivalent to linear identification of the socalled Koopman operator. Instead of considering nonlinear system identification in the state space, we obtain a novel linear…

A geometric global formulation of the higher-order Lagrangian formalism for systems with finite number of degrees of freedom is provided. The formalism is applied to the study of systems with groups of Noetherian symmetries.

A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis (the generalized Bochner problem) is given. The main result is that any operator with…

The logarithmic Laplacian on the (whole) N-dimensional Euclidean space is defined as the first variation of the fractional Laplacian of order 2s at s=0 or, alternatively, as a singular Fourier integral operator with logarithmic symbol.…

We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…

In this paper we derive structure theorems that characterize the spaces of linear and non-linear differential operators that preserve finite dimensional subspaces generated by polynomials in one or several variables. By means of the useful…

Symmetry is present in many tasks in computer vision, where the same class of objects can appear transformed, e.g. rotated due to different camera orientations, or scaled due to perspective. The knowledge of such symmetries in data coupled…

We find the Noether point symmetries for non-relativistic two-dimensional charged particle motion. These symmetries are composed of a quasi-invariance transformation, a time-dependent rotation and a time-dependent spatial translation. The…

Dynamical systems, described by Lagrangians with first- and second-class constraints, are investigated. In the Dirac approach to the generalized Hamiltonian formalism, the classification and separation of the first- and second-class…

We investigate the relation between pluri-Lagrangian hierarchies of $2$-dimensional partial differential equations and their variational symmetries. The aim is to generalize to the case of partial differential equations the recent findings…

Here we present a new approach to compute symmetries of rational second order ordinary differential equations (rational 2ODEs). This method can compute Lie symmetries (point symmetries, dynamical symmetries and non-local symmetries)…

We consider higher symmetries and operator symmetries of linear partial differential equations. The higher symmetries form a Lie algebra, and operator ones form an associative algebra. The relationship between these symmetries is…

Langrange duality theorems for vector and set optimization problems which are based on an consequent usage of infimum and supremum (in the sense greatest lower and least upper bounds with respect to a partial ordering) have been recently…

Invariant linearization criteria of square systems of second-order quadratically semi-linear ordinary differential equations (ODEs) that can be represented as geodesic equations are extended to square systems of ODEs cubically nonlinear in…

We prove Noether's direct and inverse second theorems for Lagrangian systems on fiber bundles in the case of gauge symmetries depending on derivatives of dynamic variables of an arbitrary order. The appropriate notions of reducible gauge…