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We investigate classical and semiclassical aspects of codimension--two bifurcations of periodic orbits in Hamiltonian systems. A classification of these bifurcations in autonomous systems with two degrees of freedom or time-periodic systems…
We report on a theoretical study of a Cs$_2$ molecule illuminated by two lasers and show how it can result in novel quantum dynamics. We reveal that these interactions facilitate the bypass of the non-crossing rule, forming Light-Induced…
Collision refers to a striking nonlinear interaction in dissipative systems, revealing the particle-like properties of solitons. In dual-wavelength mode-locked fiber lasers, collisions are inherent and periodic. However, how collisions…
We consider an ensemble of diatomic molecules resonantly coupled to an optical cavity under strong coupling conditions at normal incidence. Photodissociation dynamics is examined via direct numerical integration of the coupled…
We consider a diatomic molecule driven by a linearly polarized laser pulse with a polarization axis rotating with a constant acceleration. This setup is referred to as optical centrifuge, and it is known to lead to high-angular momenta for…
The bifurcation structure of coupled periodically driven double-well Duffing oscillators is investigated as a function of the strength of the driving force $f$ and its frequency $\Omega$. We first examine the stability of the steady state…
We study the destabilization mechanism in a unidirectional ring of identical oscillators, perturbed by the introduction of a long-range connection. It is known that for a homogeneous, unidirectional ring of identical Stuart-Landau…
This paper investigates the global structures of periodic orbits that appear in Rayleigh-B\'enard convection, which is modeled by a two-dimensional perturbed Hamiltonian model, by focusing upon resonance, symmetry and bifurcation of the…
The fragmentation of diatomic molecules under a stochastic force is investigated both classically and quantum mechanically, focussing on their dissociation probabilities. It is found that the quantum system is more robust than the classical…
Summary: A system of autonomous ordinary differential equations depending on a small parameter is considered such that the unperturbed system has an invariant manifold of periodic solutions that is not normally hyperbolic but is normally…
We present a general review of the bifurcation sequences of periodic orbits in general position of a family of resonant Hamiltonian normal forms with nearly equal unperturbed frequencies, invariant under $Z_2 \times Z_2$ symmetry. The rich…
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…
Dislocation-assisted phase separation processes in binary systems subjected to irradiation effect are studied analytically and numerically. Irradiation is described by athermal atomic mixing in the form of ballistic flux with spatially…
The photodissociation of the HD+ molecular ion in intense short- pulsed linearly polarized laser fields is studied using a time- dependent wave-packet approach where molecular rotation is fully included. We show that applying a coherent…
As the parameters of a piecewise-smooth system of ODEs are varied, a periodic orbit undergoes a bifurcation when it collides with a surface where the system is discontinuous. Under certain conditions this is a grazing-sliding bifurcation.…
We discuss the bifurcation structure of homoclinic orbits in bimodal one dimensional maps. The universal structure of these bifurcations with singular bifurcation points and the web of bifurcation lines through the parameter space are…
The properties of motion close to the transition of a stable family of periodic orbits to complex instability is investigated with two symplectic 4D mappings, natural extensions of the standard mapping. As for the other types of…
We derive uniform approximations for contributions to Gutzwiller's periodic-orbit sum for the spectral density which are valid close to bifurcations of periodic orbits in systems with mixed phase space. There, orbits lie close together and…
Spatial diffusion of particles in periodic potential models has provided a good framework for studying the role of chaos in global properties of classical systems. Here a bidimensional "soft" billiard, classically modeled from an optical…
A 1:2 internally resonant mechanical system can undergo secondary Hopf (Neimark-Sacker) bifurcations, resulting in a quasi-periodic response when the system is subject to harmonic excitation. While these quasi-periodic orbits have been…