Recurrence-time statistics in non-Hamiltonian volume-preserving maps and flows

Area of Science:

• Dynamical Systems
• Nonlinear Dynamics
• Statistical Physics

Background:

• Recurrence-time statistics (RTS) are crucial for understanding dynamical systems.
• Non-Hamiltonian volume-preserving systems (VPS) present complex behaviors.
• Investigating 3D systems offers insights beyond lower dimensions.

Purpose of the Study:

• Analyze RTS in 3D non-Hamiltonian VPS.
• Understand the impact of an extra dimension on system dynamics.
• Compare findings with systems involving dissipation or noise.

Main Methods:

• Extended standard map model with an extra dimension.
• Fluid model analysis.
• Classification of ordered and chaotic regimes.
• Scaling properties analysis.

Main Results:

• Extra dimension significantly enhances trapping times, creating plateaus in RTS.
• Identified distinct algebraic and exponential decays in RTS.
• Demonstrated diffusive penetration into regular islands via trapping tubes.
• Linked exponential RTS decays to quasiregular motion and conjectured mixing dynamics.

Conclusions:

• 3D VPS exhibit unique RTS features compared to systems with dissipation or noise.
• The extended standard map and fluid model show comparable RTS patterns.
• Extra dimensions profoundly alter recurrence properties in dynamical systems.