Flows and Cascades

Sergei Yu. Pilyugin
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Sergei Yu. Pilyugin: State University Petrodvorets, Bibliotechnaya pI. 2, Department of Mathematics and Mechanics

Chapter Chapter 1 in Introduction to Structurally Stable Systems of Differential Equations, 1988, pp 1-9 from Springer

Abstract: Abstract 1. Consider an autonomous system of differential equations where x ∈ ℝ n . We assume throughout the book that the function F ∈ C r (ℝ n ), r ≥ 1. Fix an arbitrary point x0 ∈ ℝ n . By the Existence and Uniqueness Theorem there exists a number h > 0 such that there is a unique solution of system (1.1) defined on (-h, h) and having the following property: The graph of the map is called the integral curve of this solution. The projection of the integral curve on the phase space ℝ n , i.e. the set, is called the trajectory of system (1.1) with initial conditions (0, x0). Throughout this book we denote this trajectory by.

Date: 1988
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DOI: 10.1007/978-3-0348-8643-7_1

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