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We discuss various bifurcation problems in which two isolated periodic orbits exchange periodic ``bridge orbit(s) between two successive bifurcations. We propose normal forms which locally describe the corresponding fixed point scenarios on the Poincare surface of section. Uniform approximations for the density of states for an integrable Hamiltonian system with two degrees of freedom are derived and successfully reproduce the numerical quantum-mechanical results.
The multiphoton ionization of hydrogen by a strong bichromatic microwave field is a complex process prototypical for atomic control research. Periodic orbit analysis captures this complexity: Through the stability of periodic orbits we can match qual
The phase-space structure of two families of galactic potentials is approximated with a resonant detuned normal form. The normal form series is obtained by a Lie transform of the series expansion around the minimum of the original Hamiltonian. Attent
We investigate the multiphoton ionization of hydrogen driven by a strong bichromatic microwave field. In a regime where classical and quantum simulations agree, periodic orbit analysis captures the mechanism: Through the linear stability of periodic
We discuss the history of the monodromy theorem, starting from Weierstrass, and the concept of monodromy group. From this viewpoint we compare then the Weierstrass , the Legendre and other normal forms for elliptic curves, explaining their geometric
In this paper we study the breakdown of normal hyperbolicity and its consequences for reaction dynamics; in particular, the dividing surface, the flux through the dividing surface (DS), and the gap time distribution. Our approach is to study these qu