Saddle-nodes and period-doublings of Smale horseshoes: a case study near resonant homoclinic bellows
Homburg, Ale Jan ; Jukes, Alice C. ; Knobloch, Jürgen ; Lamb, Jeroen S.W.
Bull. Belg. Math. Soc. Simon Stevin, Tome 15 (2008) no. 1, p. 833-850 / Harvested from Project Euclid
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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''.
Publié le : 2008-11-15
Classification:  homoclinic loop,  horseshoe,  bifurcation,  37G20,  37G30 
@article{1228486411,
     author = {Homburg, Ale Jan and Jukes, Alice C. and Knobloch, J\"urgen and Lamb, Jeroen S.W.},
     title = {Saddle-nodes and period-doublings of Smale horseshoes: a case study near resonant homoclinic bellows},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {15},
     number = {1},
     year = {2008},
     pages = { 833-850},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1228486411}
}

Homburg, Ale Jan; Jukes, Alice C.; Knobloch, Jürgen; Lamb, Jeroen S.W. Saddle-nodes and period-doublings of Smale horseshoes: a case study near resonant homoclinic bellows. Bull. Belg. Math. Soc. Simon Stevin, Tome 15 (2008) no. 1, pp.  833-850. http://gdmltest.u-ga.fr/item/1228486411/