Erratum: New integrable nonlinear integrodifferential equations and related solvable finite‐dimensional dynamical systems [J. Math. Phys. 29, 49 (1988)]

1989 ◽  
Vol 30 (1) ◽  
pp. 241-241 ◽  
Author(s):  
Y. Matsuno
Keyword(s):  
Dynamical Systems ◽  
Integrodifferential Equations ◽  
Finite Dimensional ◽  
Math Phys

Integrable two-dimensional dynamical systems and the characteristic Lie algebras

2007 ◽  
Vol 5 ◽  
pp. 195-200
Author(s):  
A.V. Zhiber ◽  
O.S. Kostrigina
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Second Order ◽  
System Of Equations ◽  
Two Dimensional ◽  
Finite Dimensional ◽  
Dimensional Dynamical System

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

Oscillations-Induced Transitions and Their Application in Control of Dynamical Systems

1990 ◽  
Vol 112 (3) ◽  
pp. 313-319 ◽  
Author(s):  
J. Bentsman
Keyword(s):  
Dynamical Systems ◽  
Parabolic Equations ◽  
Closed Loop ◽  
Distributed Parameter ◽  
Control Laws ◽  
Loop Control ◽  
Finite Dimensional ◽  
Analytical Tools ◽  
Semilinear Parabolic ◽  
Qualitative Changes

Studies of the use of oscillations for control purposes continue to reveal new practically important properties unique to the oscillatory open and closed loop control laws. The goal of this paper is to enlarge the available set of analytical tools for such studies by introducing a method of analysis of the qualitative changes in the behavior of dynamical systems caused by the zero mean parametric excitations. After summarizing and slightly refining a technique developed previously for the finite dimensional nonlinear systems, we consider an extension of this technique to a class of distributed parameter systems (DPS) governed by semilinear parabolic equations. The technique presented is illustrated by several examples.

Classification of AF Flows

2003 ◽  
Vol 46 (2) ◽  
pp. 164-177 ◽  
Author(s):  
Andrew J. Dean
Keyword(s):  
Dynamical Systems ◽  
Automorphism Group ◽  
Bratteli Diagram ◽  
Finite Dimensional

AbstractAn AF flow is a one-parameter automorphism group of an AF C*-algebra A such that there exists an increasing sequence of invariant finite dimensional sub-C*-algebras whose union is dense in A. In this paper, a classification of C*-dynamical systems of this form up to equivariant isomorphism is presented. Two pictures of the actions are given, one in terms of a modified Bratteli diagram/pathspace construction, and one in terms of a modified K0 functor.

Dynamical systems: Approximate Lagrangians and Noether symmetries

2019 ◽  
Vol 16 (10) ◽  
pp. 1950160 ◽  
Author(s):  
Sameerah Jamal
Keyword(s):  
Riemannian Manifold ◽  
Dynamical Systems ◽  
Variational Principle ◽  
Kinetic Energy ◽  
Equations Of Motion ◽  
Noether Symmetry ◽  
Noether Symmetries ◽  
Geometric Conditions ◽  
Finite Dimensional ◽  
Second Order Equations

We determine the approximate Noether point symmetries of the variational principle characterizing second-order equations of motion of a particle in a (finite-dimensional) Riemannian manifold. In particular, the Lagrangian comprises of kinetic energy and a potential [Formula: see text], perturbed to [Formula: see text]. We establish a convenient system of approximate geometric conditions that suffices for the computation of approximate Noether symmetry vectors and moreover, simplifies the problem of the effect of higher orders of the perturbation. The general results are applied to several practical problems of interest and we find extra Noether symmetries at [Formula: see text].

scholarly journals On the controllability of fractional dynamical systems

2012 ◽  
Vol 22 (3) ◽  
pp. 523-531 ◽  
Author(s):  
Krishnan Balachandran ◽  
Jayakumar Kokila
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Matrix Function ◽  
Sufficient Conditions ◽  
Schauder’S Fixed Point Theorem ◽  
Finite Dimensional ◽  
Linear And Nonlinear ◽  
Controllability Grammian

Abstract This paper is concerned with the controllability of linear and nonlinear fractional dynamical systems in finite dimensional spaces. Sufficient conditions for controllability are obtained using Schauder’s fixed point theorem and the controllability Grammian matrix which is defined by the Mittag-Leffler matrix function. Examples are given to illustrate the effectiveness of the theory.

scholarly journals Caterpillar solutions in coupled pendula

1988 ◽  
Vol 8 (8) ◽  
pp. 153-174 ◽  
Keyword(s):  
Dynamical Systems ◽  
Periodic Potential ◽  
Gordon Equation ◽  
Natural Extension ◽  
Sine Gordon Equation ◽  
Parameter Region ◽  
Intrinsic Interest ◽  
Finite Dimensional ◽  
Associated Solutions ◽  
Geometrical Explanation

AbstractThe single pendulum is one of the fundamental model problems in the theory of dynamical systems; coupled pendula, or equivalently, two elastically coupled particles in a periodic potential on a line, are a natural extension of intrinsic interest. The system arises in various physical applications and it inherits some rudiments of the behaviour exhibited by its finite-dimensional parent, the sine-Gordon equation. Among these phenomena are the so-called caterpillar solutions, whose behaviour is reminiscent of solitons. These solutions turn out to have a transparent geometrical explanation. There is an interesting bifurcation picture associated with the system: the parameter region is broken up into the set of ‘pyramids’ parametrized by pairs of integers; these integers characterize the behaviour of the associated solutions.

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