File:Poincare-Hopf.svg

Original file ‎(SVG file, nominally 512 × 512 pixels, file size: 264 KB)

This is a file from the Wikimedia Commons. The description on its description page there is shown below.
Commons is a freely licensed media file repository. You can help.

Summary

DescriptionPoincare-Hopf.svg	Polski: 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. $H(x,y)=\exp(-(x-1)^{2}-y^{2})+\exp(-(x+1)^{2}-y^{2})$ English: 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. $H(x,y)=\exp(-(x-1)^{2}-y^{2})+\exp(-(x+1)^{2}-y^{2})$ )
Date	14 November 2018
Source	Own work
Author	Radost Waszkiewicz

I, the copyright holder of this work, hereby publish it under the following license:

	This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
	The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission. CC0falsefalse

Click on a date/time to view the file as it appeared at that time.

	Date/Time	Thumbnail	Dimensions	User	Comment
current	20:25, 14 November 2018		512 × 512 (264 KB)	RadostW	User created page with UploadWizard

The following page uses this file:

The following other wikis use this file:

This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.

If the file has been modified from its original state, some details may not fully reflect the modified file.

Width	100%
Height	100%