An Elementary Proof of the Jordan Curve Theorem and its Application to the Poincaré-Bendixson Theorem
(2021) In Bachelor's Theses in Mathematical Sciences MATK11 20211Mathematics (Faculty of Engineering)
Mathematics (Faculty of Sciences)
- Abstract
- This thesis is mainly focused on a proof of the Jordan Curve Theorem. We follow Tverberg’s paper: A PROOF OF THE JORDAN CURVE THEOREM, but add some more details and graphics in order to make this topological proof more understandable. Later in this thesis, the proof of the Poincare-Bendixson Theorem will also be discussed, as an application of the Jordan Curve Theorem.
- Popular Abstract
- Imagine that you draw a curve on a paper. If the curve forms a closed loop without self-intersecting, then it will divide the paper into two parts, the interior and the exterior. This is what the Jordan curve theorem says. While it may seem self-evident, the proof is actually not that simple. Mathematicians have developed several different ways of proving it. This thesis follows Tverberg’s paper "A PROOF OF THE JORDAN CURVE THEOREM" but using graphics to demonstrate and make the proof easier to understand. The Poincaré-Bendixson theorem states the long-term behavior of an orbit of a continuous dynamical system in the plane. The Jordan curve theorem plays an important role in proving this theorem and the thesis explains how.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9063529
- author
- Zhu, Yining LU
- supervisor
-
- Erik Wahlén LU
- Jörg Weber LU
- organization
- course
- MATK11 20211
- year
- 2021
- type
- M2 - Bachelor Degree
- subject
- keywords
- Jordan Curve Theorem, Poincaré-Bendixson Theorem
- publication/series
- Bachelor's Theses in Mathematical Sciences
- report number
- LUNFMA-4123-2021
- ISSN
- 1654-6229
- other publication id
- 2021:K33
- language
- English
- id
- 9063529
- date added to LUP
- 2024-04-15 16:24:16
- date last changed
- 2024-04-15 16:24:16
@misc{9063529, abstract = {{This thesis is mainly focused on a proof of the Jordan Curve Theorem. We follow Tverberg’s paper: A PROOF OF THE JORDAN CURVE THEOREM, but add some more details and graphics in order to make this topological proof more understandable. Later in this thesis, the proof of the Poincare-Bendixson Theorem will also be discussed, as an application of the Jordan Curve Theorem.}}, author = {{Zhu, Yining}}, issn = {{1654-6229}}, language = {{eng}}, note = {{Student Paper}}, series = {{Bachelor's Theses in Mathematical Sciences}}, title = {{An Elementary Proof of the Jordan Curve Theorem and its Application to the Poincaré-Bendixson Theorem}}, year = {{2021}}, }