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Flows and Cascades

In: Introduction to Structurally Stable Systems of Differential Equations

Author

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  • Sergei Yu. Pilyugin

    (State University Petrodvorets, Bibliotechnaya pI. 2, Department of Mathematics and Mechanics)

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.

Suggested Citation

  • Sergei Yu. Pilyugin, 1988. "Flows and Cascades," Springer Books, in: Introduction to Structurally Stable Systems of Differential Equations, chapter 0, pages 1-9, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-8643-7_1
    DOI: 10.1007/978-3-0348-8643-7_1
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