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Full-Text Articles in Physical Sciences and Mathematics
The Zorich Transform And Generalizing Koenigs Linearization Theorem To Quasiregular Maps, Jacob A. Pratscher
The Zorich Transform And Generalizing Koenigs Linearization Theorem To Quasiregular Maps, Jacob A. Pratscher
Graduate Research Theses & Dissertations
This dissertation investigates the role that a new tool called the Zorich transform plays in quasiregular dynamics as a generalization of the logarithmic transform in complex dynamics. In particular we use the Zorich transform to construct analogues of the logarithmic spiral maps and interpolation between radial stretch maps. These constructions are then used to completely classify the orbit space of a quasiregular map. Also, conditions are given in which a quasiregular map $f:D\to\R^n$, where $D\subset\R^n$ is a domain, that is quasiconformal in a neighborhood of a geometrically attracting fixed point can be conjugated by a quasiconformal map to the asymptotic …
Model-Based Network Reconstruction From Cascade Dynamics, Katherine Irena Chwistek
Model-Based Network Reconstruction From Cascade Dynamics, Katherine Irena Chwistek
Graduate Research Theses & Dissertations
Network representation provides a natural framework for the study of real world complex systems. From social networks and animal groups to interneuronal communications and power grid systems, complex patterns of interaction can be captured and modeled using networks in a simple mathematical form. In many cases, however, a faithful network representation of the system is not readily available. For this reason, network reconstruction has become a growing topic of interest in recent years, the goal of which is to discover the hidden interaction patterns among individuals by fitting input-output data from multiple experiments to candidate network topologies.
During a cascade, …
A Spider's Web Of Doughnuts, Daniel Stoertz
A Spider's Web Of Doughnuts, Daniel Stoertz
Graduate Research Theses & Dissertations
This dissertation studies an interplay between the dynamics of iterated quasiregular map-
pings and certain topological structures. In particular, the relationship between the Julia set
of a uniformly quasiregular mapping f : R 3 → R 3 and the fast escaping set of its associated
Poincaré linearizer is explored. It is shown that, if the former is a Cantor set, then the latter
is a spider’s web. A new class of uniformly quasiregular maps is constructed to which this
result applies. Toward this, a geometrically self-similar Cantor set of genus 2 is constructed.
It is also shown that for any …