Saddle-nodes and period-doublings of Smale horseshoes: a case study near resonant homoclinic bellows | Zendy

Ale Jan Homburg | Zendy; Alice C. Jukes | Zendy; Jürgen Knobloch | Zendy; Jeroen S. W. Lamb | Zendy

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Saddle-nodes and period-doublings of Smale horseshoes: a case study near resonant homoclinic bellows

Author(s) -

Ale Jan Homburg,

Alice C. Jukes,

Jürgen Knobloch,

Jeroen S. W. Lamb

Publication year - 2008

Publication title -

bulletin of the belgian mathematical society - simon stevin

Language(s) - English

Resource type - Journals

eISSN - 2034-1970

pISSN - 1370-1444

DOI - 10.36045/bbms/1228486411

Subject(s) - homoclinic orbit , saddle , bifurcation , homoclinic bifurcation , period (music) , node (physics) , periodic orbits , horseshoe (symbol) , physics , saddle node bifurcation , mathematics , classical mechanics , computer science , mathematical optimization , nonlinear system , quantum mechanics , programming language , acoustics

In unfoldings of resonant homoclinic bellows interesting bifurcation phenomena occur: two suspensed Smale horseshoes can collide and disappear in saddle-node bifurcations (all periodic orbits disappear through saddle-node bifurcations, there are no other bifurcations of periodic orbits), or a suspended horseshoe can go through saddle-node and period-doubling bifurcations of the periodic orbits in it to create an additional "doubled horseshoe".

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