36 citations · 243 across the 29 of their papers we have counts for
12 papers · 1 filter
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…
Analytic approach to bifurcation cascades in a class of generalized Hénon-Heiles potentials
S. N. Fedotkin, A. G. Magner, M. Brack
We derive stability traces of bifurcating orbits in Hénon-Heiles potentials near their saddles
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…
Transcritical bifurcations in non-integrable Hamiltonian systems
Matthias Brack, Kaori Tanaka
We report on transcritical bifurcations of periodic orbits in non-integrable two-dimensional Hamiltonian systems. We discuss their existence criteria and some of their properties u…
Effect of pitchfork bifurcations on the spectral statistics of Hamiltonian systems
Marta Gutiérrez, Matthias Brack, Klaus Richter +1
We present a quantitative semiclassical treatment of the effects of bifurcations on the spectral rigidity and the spectral form factor of a Hamiltonian quantum system defined by tw…
Level density of the Hénon-Heiles system above the critical barrier Energy
M. Brack, J. Kaidel, P. Winkler +1
We discuss the coarse-grained level density of the Hénon-Heiles system above the barrier energy, where the system is nearly chaotic. We use periodic orbit theory to approximate its…