PhD ceremony Mr. Ü. Ciftci: Cotangent bundle reduction and its applications to Poincare-Birkhoff normal forms. Analysis of reactions in rotating molecules

PhD ceremony: Mr. Ü. Ciftci, 9.00 uur, Academiegebouw, Broerstraat 5, Groningen

Dissertation: Cotangent bundle reduction and its applications to Poincare-Birkhoff normal forms. Analysis of reactions in rotating molecules

Promotor(s): prof. H. Waalkens

Faculty: Mathematics and Natural Sciences

The main concern of this thesis work is the study of reaction type dynamics in rotating molecules. As rotations almost always play a role in the reaction of molecules the study of reaction type dynamics induced by saddle type relative equilibria is of great importance for applications. In Chapter 2, we study a systematic and natural construction of canonical coordinates for the reduced space of a cotangent bundle with a free Lie group action. The canonical coordinates enable us to compute Poincaré-Birkhoff normal forms of relative equilibria using standard algorithms. The case of simple mechanical systems with symmetries is studied in detail. As examples we compute Poincaré-Birkhoff normal forms for a Lagrangian equilateral triangle configuration of a three-body system with a Morse-type potential and the stretched-out configuration of a double spherical pendulum. After that we show in Chapter 3 how the construction of phase space structures can be generalized to the case of the relative equilibria of a rotational symmetry reduced three-body system. Then the rotational reaction dynamics of an HCN molecule is analyzed in detail. In Chapter 4, we point out a new type of bottleneck which mediates kinetic rather than configurational changes. In Chapter 5, we suggest that the translation-reduced configuration space of a triatomic system may be considered as the reduced holonomy bundle with a connection induced by the mechanical connection.