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nlin.CD2008★ 10 cited
Normal forms and uniform approximations for bridge orbit bifurcations
Ken-ichiro Arita, Matthias Brack
We discuss various bifurcation problems in which two isolated periodic orbits exchange periodic ``bridge'' orbit(s) between two successive bifurcations. We propose normal forms whi…
nlin.CD2007★ 7 cited
Anomalous shell effect in the transition from a circular to a triangular billiard
Ken-ichiro Arita, Matthias Brack
We apply periodic orbit theory to a two-dimensional non-integrable billiard system whose boundary is varied smoothly from a circular to an equilateral triangular shape. Although th…