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According to Poincare-Hopf theorem closed trajectory can encircle two centres and one saddle or one centre but never just the saddle. (Here for a Hamiltonian system with Hamiltonian being sum of two Gaussians.
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Zgodnie z twierdzeniem Poincarego-Hopfa zamknięta orbita może otaczać jedno ognisko, lub dwa ogniska i jedno siodło, nigdy jednak wyłącznie dwa ogniska ani wyłącznie jedno siodło.
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File:Poincare-Hopf.svg
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480 × 480 pixels
768 × 768 pixels
1,024 × 1,024 pixels
2,048 × 2,048 pixels
Original file
Wikimedia Commons
description page there
You can help
Radost Waszkiewicz
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