The Second Part of Hilbert’s Sixteenth Problem

Stephen Lynch ()
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Stephen Lynch: Manchester Metropolitan University, Department of Computing and Mathematics

Chapter 10 in Dynamical Systems with Applications using Maple¿, 2010, pp 219-241 from Springer

Abstract: Aims and Objectives • To describe the second part of Hilbert’s sixteenth problem. • To reviewthe main results on the number of limit cycles of planar polynomial systems. • To consider the flow at infinity after Poincaré compactification. • To review the main results on the number of limit cycles of Liénard systems. • To prove two theorems concerning limit cycles of certain Liénard systems. On completion of this chapter, the reader should be able to • state the second part of Hilbert’s sixteenth problem; • describe the main results for this problem; • compactify the plane and construct a global phase portrait which shows the behavior at infinity for some simple systems; • compare local and global results; • prove that certain systems have a unique limit cycle; • prove that a limit cycle has a certain shape for a large parameter value.

Date: 2010
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DOI: 10.1007/978-0-8176-4605-9_11

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