Neo-adjuvant chemotherapy followed by surgery versus surgery alone in high-risk patients with resectable colorectal liver metastases: The CHARISMA randomized multicenter clinical trial

Background: Efforts to improve the outcome of liver surgery by combining curative resection with chemotherapy have failed to demonstrate de

Reduction and regularization of the Kepler problem

The KS regularization connects the dynamics of the harmonic oscillator to the dynamics of bounded Kepler orbits. Using orbit space reduction, it can be shown that reduced harmonic oscillator orbits can be identified with re-parametrized Kepler orbits by factorizing the KS map as reduction mapping followed by a chart on the reduced phase space. In this note, we will show that also other regularization maps can be obtained this way. In particular, we will show how Moser’s regularization and Ligon–Schaaf regularization are related to KS-regularization. All regularizations are a result of choosing the right invariants to represent the reduced phase space, which is isomorphic to T+S3, and a chart on this reduced phase space. We show how this opens the way to directly reduce the KS transformed Kepler system and find other regularization maps that are valid for all values of the Keplerian energy similar to Ligon–Schaaf regularization

Book review: Global aspects of classical integrable systems

No abstract

Book review: Global aspects of classical integrable systems

Geen samenvatting

Algebraic methods for determining Hamiltonian Hopf bifurcations in three-degree-of-freedom systems

When considering bifurcations, the type of bifurcation is usually classi ed by comparing to standard situations or normal forms. It is shown how Hamiltonian Hopf bifurcations can be determined in three{degree{of{freedom systems, as is done in this paper for the 3D Henon{Heiles family. After a careful formulation of the local once reduced system in terms of properly chosen invariants the system can be compared to the standard form to determine the presence of non{degenerate Hamiltonian Hopf bifurcations

Orbiting dust under radiation pressure

In this paper we consider a perturbed Keplerian system describing orbiting dust under radiation pressure. We derive an integrable second order normal form for this Hamiltonian system. Finally we analyze this integrable system by successive reduction to a one degree of freedom sysyem

Generalized Hopf fibration and geometric SO(3) reduction of the 4DOF harmonic oscillator

It is shown that the generalized Hopf map H x H ¿ H x R x R in quaternion formulation can be interpreted as an SO(3) orbit map for a symplectic SO(3) action. As a consequence the generalized Hopf fibration S^7 ¿ S^4 appears in the SO(3) geometric symplectic reduction of the 4DOF isotropic harmonic oscillator. Keywords: Hopf map, Hopf fibration, symplectic reduction, harmonic oscillator