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Irreduktibilität und Monodromiegruppe algebraischer GleichungenKneser, Adolf, January 1900 (has links)
Thesis (doctoral)--Friedrich-Wilhelms-Universität zu Berlin, 1884. / Vita.
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Geometry of two degree of freedom integrable Hamiltonian systems.Zou, Maorong. January 1992 (has links)
In this work, several problems in the field of Hamiltonian dynamics are studied. Chapter 1 is a short review of some basic results in the theory of Hamiltonian dynamics. In chapter 2, we study the problem of computing the geometric monodromy of the torus bundle defined by integrable Hamiltonian systems. We show that for two degree of freedom systems near an isolated critical value of the energy momentum map, the monodromy group can be determined solely from the local data of the energy momentum map at the singularity. Along the way, we develop a simple method for computing the monodromy group which covers all the known examples that exhibit nontrivial monodromy. In chapter 3, we consider the topological aspects of the Kirchhoff case of the motion of a symmetric rigid body in an infinite ideal fluid. The bifurcation diagrams are constructed and the topology of all the invariant sets are determined. We show that this system has monodromy. We show also that this system undergoes a Hamiltonian Hopf bifurcation as the couple resultant passes through a certain value when the steady rotation of the rigid body about its symmetry axis changes stability. Chapter 4 is devoted to checking Kolmogorov's condition for the square potential pendulum. We prove, by essentially elementary methods, that Kolmogorov's condition is satisfied for all of the regular values of the energy momentum map. In chapter 5, we use Ziglin's theorem to prove rigorously that some of the generalized two degree of freedom Toda lattices are non-integrable.
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Monodromies of torsion D-branes on Calabi-Yau manifolds: extending the Douglas, et al., programMahajan, Rahul Saumik 28 August 2008 (has links)
Not available / text
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Monodromies of hyperelliptic families of genus three curves /Ishizaka, Mizuho. January 2001 (has links)
Univ., Diss.--Sendai.
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Monodromies of torsion D-branes on Calabi-Yau manifolds extending the Douglas, et al., program /Mahajan, Rahul Saumik. January 2002 (has links) (PDF)
Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.
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Asymptotic, Algorithmic and Geometric Aspects of Groups Generated by AutomataSavchuk, Dmytro M. 14 January 2010 (has links)
This dissertation is devoted to various aspects of groups generated by automata. We
study particular classes and examples of such groups from different points of view. It
consists of four main parts.
In the first part we study Sushchansky p-groups introduced in 1979 by
Sushchansky in "Periodic permutation p-groups and the unrestricted Burnside
problem". These groups represent one of the earliest examples of Burnside groups
and, at the same time, show the potential of the class of groups generated by automata
to contain groups with extraordinary properties. The original definition is translated
into the language of automata. The original actions of Sushchansky groups on p-
ary tree are not level-transitive and we describe their orbit trees. This allows us
to simplify the definition and prove that these groups admit faithful level-transitive
actions on the same tree. Certain branch structures in their self-similar closures
are established. We provide the connection with so-called G groups introduced by
Bartholdi, Grigorchuk and Suninc in "Branch groups" that shows that all Sushchansky
groups have intermediate growth and allows us to obtain an upper bound on their
period growth functions.
The second part is devoted to the opposite question of realization of known
groups as groups generated by automata. We construct a family of automata with n states, n greater than or equal to 4, acting on a rooted binary tree and generating the free products of
cyclic groups of order 2.
The iterated monodromy group IMG(z2+i) of the self-map of the complex plain
z -> z2 + i is the central object of the third part of dissertation. This group acts
faithfully on the binary rooted tree and is generated by 4-state automaton. We provide
a self-similar measure for this group giving alternative proof of its amenability. We
also compute an L-presentation for IMG(z2+i) and provide calculations related to the
spectrum of the Markov operator on the Schreier graph of the action of IMG(z2 + i)
on the orbit of a point on the boundary of the binary rooted tree.
Finally, the last part is discussing the package AutomGrp for GAP system developed
jointly by the author and Yevgen Muntyan. This is a very useful tool for studying
the groups generated by automata from the computational point of view. Main
functionality and applications are provided.
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