Near threshold anomalous transport in the standard map.

Area of Science:

• Nonlinear dynamics
• Statistical physics
• Chaos theory

Background:

• Anomalous transport phenomena are crucial in understanding complex dynamical systems.
• The standard map is a fundamental model for studying chaotic dynamics and transport.
• Investigating behavior near the threshold of chaos is key to uncovering complex transport mechanisms.

Purpose of the Study:

• To investigate anomalous transport near the threshold in the standard map.
• To identify the underlying structures responsible for unusual transport behavior.
• To characterize the phase space structure and associated exponents of these trapping mechanisms.

Main Methods:

• Analysis of the standard map dynamics near the transition to chaos.
• Identification and characterization of multi-island structures.
• Determination of phase space structures and time-tail exponents.

Main Results:

• Discovery of novel multi-island structures responsible for orbit sticking.
• Observation of very long time flights and significant anomalies in transport.
• Characterization of the phase space complexity and associated exponents of trapping structures.
• Demonstration that some layered island structures allow for simplified modeling.

Conclusions:

• Multi-island structures are a primary cause of anomalous transport and long time flights in the standard map near threshold.
• The detailed structure and exponents of these traps can be determined, offering insights into their dynamics.
• While generally complex, certain layered island structures provide a basis for tractable theoretical models.