Braids and differential equations
نویسنده
چکیده
Forcing theorems based on topological features of invariant sets have played a fundamental role in dynamics and differential equations. This talk focuses on the recent work of Vandervorst, Van den Berg, and the author using braids to construct a forcing theory for scalar parabolic PDEs, second-order Lagrangian ODEs, and one-dimensional lattice dynamics. Mathematics Subject Classification (2000). Primary 37B30, 35K90; Secondary 34C25, 37L60, 57M25.
منابع مشابه
Dynamical Systems on Three Manifolds Part I: Knots, Links and Chaos
In this paper, we give an explicit construction of dynamical systems (defined within a solid torus) containing any knot (or link) and arbitrarily knotted chaos. The first is achieved by expressing the knots in terms of braids, defining a system containing the braids and extending periodically to obtain a system naturally defined on a torus and which contains the given knotted trajectories. To g...
متن کاملHigher categories, strings, cubes and simplex equations
Abstract. This survey of categorical structures, occurring naturally in mathematics, physics and computer science, deals with monoidal categories; various structures in monoidal categories; free monoidal structures; Penrose string notation; 2-dimensional categorical structures; the simplex equations of field theory and statistical mechanics; higher-order categories and computads; the (v,d)-cube...
متن کاملSolving the liner quadratic differential equations with constant coefficients using Taylor series with step size h
In this study we produced a new method for solving regular differential equations with step size h and Taylor series. This method analyzes a regular differential equation with initial values and step size h. this types of equations include quadratic and cubic homogenous equations with constant coeffcients and cubic and second-level equations.
متن کاملExistence and continuous dependence for fractional neutral functional differential equations
In this paper, we investigate the existence, uniqueness and continuous dependence of solutions of fractional neutral functional differential equations with infinite delay and the Caputo fractional derivative order, by means of the Banach's contraction principle and the Schauder's fixed point theorem.
متن کاملReduction of Differential Equations by Lie Algebra of Symmetries
The paper is devoted to an application of Lie group theory to differential equations. The basic infinitesimal method for calculating symmetry group is presented, and used to determine general symmetry group of some differential equations. We include a number of important applications including integration of ordinary differential equations and finding some solutions of partial differential equa...
متن کامل