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To describe the second part of Hilbert’s sixteenth problem. To review the 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.

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The Second Part of Hilbert’s Sixteenth Problem

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  • 发表日期：

    2025年

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  • Stephen Lynch

摘要

To describe the second part of Hilbert’s sixteenth problem. To review the 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.