9 citations · 31 across the 7 of their papers we have counts for
7 papers
An Overview of the Relationship between Group Theory and Representation Theory to the Special Functions in Mathematical Physics
Ryan D. Wasson, Robert Gilmore
Advances in mathematical physics during the 20th century led to the discovery of a relationship between group theory and representation theory with the theory of special functions.…
Connecting Curves in Higher Dimensions
Greg Byrne, Juan Cebral, Robert Gilmore
Connecting curves have been shown to organize the rotational structure of strange attractors in three-dimensional dynamical systems. We extend the description of connecting curves…
Peeling Bifurcations of Toroidal Chaotic Attractors
Christophe Letellier, Robert Gilmore, Timothy Jones
Chaotic attractors with toroidal topology (van der Pol attractor) have counterparts with symmetry that exhibit unfamiliar phenomena. We investigate double covers of toroidal attrac…
Embeddings of low-dimensional strange attractors: Topological invariants and degrees of freedom
Nicola Romanazzi, Marc Lefranc, Robert Gilmore
When a low dimensional chaotic attractor is embedded in a three dimensional space its topological properties are embedding-dependent. We show that there are just three topological…
Global Topology from an Embedding
Robert Gilmore, Christophe Letellier, Nicola Romanazzi
An embedding of chaotic data into a suitable phase space creates a diffeomorphism of the original attractor with the reconstructed attractor. Although diffeomorphic, the original a…
Quantum Mechanical Reflection Resonances
Erica Caden, Robert Gilmore
Resonances in the reflection probability amplitude r(E) can occur in energy ranges in which the reflection probability R(E)=|r(E)|^2 is 1. They occur as the phase phi(E) defined by…