No description available.

Univ., Diss.--Sendai, 1999.

Thesis (D. Sc.)--Tohoku University. 1999. / "December 1999." Includes bibliographical references (p. 83-84).

We introduce the naive notion of a relative open book decomposition for contact 3-manifolds with torus boundary. We then use this to construct nice, minimal genus open book decompositions compatible with all of the universally tight contact structures (as well as a few others) on torus-bundles over S¹, following Honda's classification. In an accurate sense, we find Stein fillings of 'half' of the torus bundles. In addition, these give the first examples of open books compatible with the universally tight contact structures on circle bundles over higher genus surfaces, as well, following a pattern introduced by a branched covering of B⁴. Some interesting examples of open books without positive monodromy are emphasized.

No description available.

The main principle of this thesis is to employ the geometric representation of Hamiltonian dynamics: in a broad sense, we study how to construct, in phase space, geometric structures that are related to a dynamical system. More specifically, we study the problem of constructing phase-space tori that are approximate invariant tori of a given Hamiltonian; also, using the constructed tori, we define an integrable Hamiltonian closely approximating the original one. The methods are generally applicable; as examples, we use gravitational potentials that are of interest in stellar dynamics. First, we construct tori for box and loop orbits in planar, barred potentials, thus demonstrating the applicability of the scheme to potentials that have more than one major orbit family. Also, we show that, in general, the construction scheme needs two types of canonical transformations together: point transformations as well as those expressed by generating functions. To complete the construction scheme, we show how to furnish the tori with consistent coordinate systems, i.e., how to recover the angle variables of a torus labelled by its actions. Next, the developed methods are employed in creating invariant phase-space tori in nonintegrable potentials supporting minor-orbit families. These tori are used to define an integrable Hamiltonian H₀, and a modified form of the standard Hamiltonian perturbation theory is then used to demonstrate that a minor-orbit family can be treated as one made up of orbits trapped by a resonance of H₀. Finally, we generalize the scheme further by constructing tori in time-reversal asymmetric Hamiltonians (by considering the motion in a rotating frame of reference), and study the transition from locally contained stochasticity to global chaos. Using both near-integrable 'laboratory' Hamiltonians and those for which we construct tori, we investigate the transition in the light of the resonance overlap criterion.

Thesis (doctoral)--Bonn, 1997. / "Oktober 1997"--T.p. Includes bibliographical references (p. 150-153).

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 2001. / Vita. Includes bibliographical references. Available also from UMI/Dissertation Abstracts International.