Related papers: Relative Critical Points

An interesting family of geometric integrators for Lagrangian systems can be defined using discretizations of the Hamilton's principle of critical action. This family of geometric integrators is called variational integrators. In this…

The Lie algebroids are generalization of the Lie algebras. They arise, in particular, as a mathematical tool in investigations of dynamical systems with the first class constraints. Here we consider canonical symmetries of Hamiltonian…

We show that any Lie point symmetry of semilinear Kohn-Laplace equations on the Heisenberg group H^1 with power nonlinearity is a divergence symmetry if and only if the corresponding exponent assumes critical value.

We review results concerning the critical behavior of spin systems at equilibrium. We consider the Ising and the general O($N$)-symmetric universality classes, including the $N\to 0$ limit that describes the critical behavior of…

Arithmetic operations can be defined in various ways, even if one assumes commutativity and associativity of addition and multiplication, and distributivity of multiplication with respect to addition. In consequence, whenever one encounters…

The Hamiltonian description for a wide class of mechanical systems, having local symmetry transformations depending on time derivatives of the gauge parameters of arbitrary order, is constructed. The Poisson brackets of the Hamiltonian and…

In this paper, we argue in favor of first-order homogeneous Lagrangians in the velocities. The relevant form of such Lagrangians is discussed and justified physically and geometrically. Such Lagrangian systems possess Reparametrization…

Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…

Following our recent conjecture to model the phenomenona of antiferromagnetism and superconductivity by quantum symmetry groups, we discuss in the present note how to construct a workable scenario using this symmetry. In particular we…

Symmetric teleparallel gravity is one among the general relativistic trinity which deals with the non-metricity scalar $Q$. In the Einstein Hilbert action, a function of $Q$ is chosen to be the main contributory part of the Lagrangian and a…

We consider bifurcation of critical points from a trivial branch for families of functionals that are invariant under the orthogonal action of a compact Lie group. Based on a recent construction of an equivariant spectral flow by the…

We study the topology of orbits of dynamical systems defined by finite-dimensional representations of nilpotent Lie groups. Thus, the following dichotomy is established: either the interior of the set of regular points is dense in the…

We derive the dynamics of several rigid bodies of arbitrary shape in a 2-dimensional inviscid and incompressible fluid, whose vorticity field is given by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive the…

This is the first of a couple of papers in which, by exploiting the capabilities of the Hamiltonian approach to general relativity, we get a number of technical achievements that are instrumental both for a disclosure of \emph{new} results…

We construct a family of globally defined dynamical systems for a nonlinear programming problem, such that: (a) the equilibrium points are the unknown (and sought) critical points of the problem, (b) for every initial condition, the…

The multiplicative Lagrangian and Hamiltonian introduce an additional parameter that, despite its variation, results in identical equations of motion as those derived from the standard Lagrangian. This intriguing property becomes even more…

Over an algebraically closed field of positive characteristic, there exist rational functions with only one critical point. We give an elementary characterization of these functions in terms of their continued fraction expansions. Then we…

We study the set of critical points of a solution to $\Delta u = \lambda \cdot u$ and in particular components of the critical set that have codimension 1. We show, for example, that if a second Neumann eigenfunction of a simply connected…

The equations for the critical points of the action functional defined by a Lagrangian depending on higher-order derivatives of admissible curves on a Lie algebroid are found. The relation with Euler-Poincar\'e and Lagrange Poincar\'e type…

This article reveals an analysis of the quadratic systems that hold multiparametric families therefore, in the first instance the quadratic systems are identified and classified in order to facilitate their study and then the stability of…