Bifurcation of Dividing Surfaces Constructed from Period-Doubling Bifurcations of Periodic Orbits in a Caldera Potential Energy Surface

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 perioddoubling 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.

Figures (12)

• Figure 1: Plot of the PES given in Eq. (\ref{['PES']}).
• Figure 2: The coordinate $x$ (in the Poincaré section $y=0$ with $p_y>0$) of the periodic orbits of the family of the well and its bifurcations. The stable and unstable parts of the families are depicted by red and cyan colors, respectively. P1 and P2 are the points of bifurcation for the supercritical and subcritical cases, respectively.
• Figure 3: 2D projections of the periodic orbits of the family of the well in the configuration space for energies A) 0.1 B) 5 C) 10 D) 15 E) 20 F) 25 G) 28 H) 30 I) 32 J) 34.
• Figure 4: 2D projections of the periodic orbits of the first period-doubling bifurcation of the family of the well in the configuration space for energies A) 22 B) 24 C) 26 D) 28 E) 30 F) 32 G) 34.
• Figure 5: 2D projections of the periodic orbits of the second period-doubling bifurcation of the family of the well in the configuration space for energies A) 30 B) 32 C) 34.