6533b828fe1ef96bd1287838
RESEARCH PRODUCT
On the saddle loop bifurcation
Freddy DumortierRobert Roussariesubject
PhysicsSaddle pointMathematical analysisModulusVector fieldBifurcation diagramEngineering physicsBifurcationStable manifoldSaddledescription
It is shown that the set of C∞ (generic) saddle loop bifurcations has a unique modulus of stability γ ≥]0, 1[∪]1, ∞[ for (C0, Cr)-equivalence, with 1≤r≤∞. We mean for an equivalence (x,μ) ↦ (h(x,μ), ϕ(μ)) with h continuous and ϕ of class Cr. The modulus γ is the ratio of hyperbolicity at the saddle point of the connection. Already asking ϕ to be a lipeomorphism forces two saddle loop bifurcations to have the same modulus, while two such bifurcations with the same modulus are (C0,±Identity)-equivalent.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1990-01-01 |