Irregular period-tripling bifurcations in axisymmetric scalefree potentials

Area of Science:

• Dynamical systems theory
• Celestial mechanics
• Nonlinear dynamics

Background:

• Axisymmetric potentials are fundamental in modeling various physical systems, including galactic dynamics.
• Understanding orbital dynamics and bifurcations is crucial for accurate modeling.
• Irregular bifurcations can lead to complex and unpredictable behaviors in dynamical systems.

Purpose of the Study:

• To investigate the phenomenon of irregular bifurcations in axisymmetric scale-free potentials.
• To understand the formation and significance of a new family of orbits with period 3.
• To elucidate the relationship between these bifurcations and the rotation number of phase-space tori.

Main Methods:

• Analysis of bifurcations in axisymmetric scale-free potentials.
• Examination of the transition of the rotation number of phase-space tori.
• Comparison with the behavior of nontwist maps.

Main Results:

• A new family of orbits with period 3 arises from tube orbits during irregular bifurcations.
• These bifurcations are directly linked to the rotation number of the phase-space torus transitioning through 1/3.
• The identified bifurcations share similarities with those observed in nontwist maps.

Conclusions:

• Irregular bifurcations in axisymmetric scale-free potentials generate significant new orbital structures.
• The transition of the rotation number to 1/3 is a critical indicator for these bifurcations.
• This research provides insights into the complex dynamics of nontwist maps and their relevance in physical models.