Drift-Controlled Density Regimes in kx+1 Dynamical Systems: Ensemble Magnitude Growth and Coalescence Under N-Scaling

Key Points

• The study aims to explore how ensemble dynamics behave in kx+1 dynamical systems under N-scaling.
• Conducted computational simulations of ensemble dynamics in generalized kx+1 maps.
• Examined dynamics for k values of 3 and 4 with varying N-scaling.
• Analyzed collision densities and magnitude growth patterns up to N=200,000 and T=160.
• For k=3, the system exhibits bounded magnitude with persistent collision density.
• For k≥4, magnitude expands but collision density dilutes.
• Significant differences in density regimes are observed based on the value of k.