- Tytuł:
- A proof of the two-dimensional Markus-Yamabe Stability Conjecture and a generalization
- Autorzy:
- Feßler, Robert
- Powiązania:
- https://bibliotekanauki.pl/articles/1311487.pdf
- Data publikacji:
- 1995
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
Markus-Yamabe conjecture
asymptotic behaviour of solutions of ODE's
immersions
embeddings
injectivity of mappings
curve lifting
foliations - Opis:
- The following problem of Markus and Yamabe is answered affirmatively: Let f be a local diffeomorphism of the euclidean plane whose jacobian matrix has negative trace everywhere. If f(0) = 0, is it true that 0 is a global attractor of the ODE dx/dt = f(x)? An old result of Olech states that this is equivalent to the question if such an f is injective. Here the problem is treated in the latter form by means of an investigation of the behaviour of f near infinity.
- Źródło:
-
Annales Polonici Mathematici; 1995, 62, 1; 45-74
0066-2216 - Pojawia się w:
- Annales Polonici Mathematici
- Dostawca treści:
- Biblioteka Nauki
Artykuł