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RESEARCH PRODUCT

Families of Two-dimensional Vector Fields

Robert Roussarie

subject

Section (fiber bundle)Pure mathematicsBifurcation theoryFlow (mathematics)Phase portraitPhase spaceVector fieldUniquenessSingular point of a curveMathematics

description

In this section we will consider individual vector fields. They can be considered as 0-parameter families. We assume these vector fields to be of class at least C 1. This will be sufficient to ensure the existence and uniqueness of the flow φ(t, x) (t is time, x ∈ S, the phase space) and the qualitative properties which we mention below.

https://doi.org/10.1007/978-3-0348-8798-4_1