Bifurcation of Dividing Surfaces Constructed from Period-Doubling Bifurcations of Periodic Orbits in a Caldera Potential Energy Surface
Matthaios Katsanikas, Makrina Agaoglou, Stephen Wiggins
Abstract
In this work we analyze the bifurcation of dividing surfaces that occurs as a result of two period-doubling bifurcations in a 2D caldera-type potential. We study the structure, the range, the minimum and maximum extents of the periodic orbit dividing surfaces before and after a subcritical period-doubling bifurcation of the family of the central minimum of the potential energy surface. Furthermore, we repeat the same study for the case of a supercritical period-doubling bifurcation of the family of the central minimum of the potential energy surface. We will discuss and compare the results for the two cases of bifurcations of dividing surfaces.
Topics & Concepts
BifurcationPeriod-doubling bifurcationCalderaSurface (topology)Period (music)MathematicsPitchfork bifurcationWork (physics)GeometryNonlinear systemPhysicsBifurcation theoryGeologyThermodynamicsQuantum mechanicsAcousticsSeismologyVolcanoQuantum chaos and dynamical systemsGeometric Analysis and Curvature FlowsAstro and Planetary Science