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All conservative nonintegrable classical systems, with three or more degrees of freedom (DoF), can undergo a global transition to chaos due to a dense web of resonances (the Arnol’d web) that permeates the phase space. Each resonance line in the Arnol’d web is surrounded by a resonance region and a stochastic web. The system can diffuse throughout each energy surface, both along and across the web in a universal diffusion process called Arnol’d diffusion. The rate of diffusion depends on parameters of the system. Because Arnol’d diffusion occurs in systems with three or more degrees of freedom, it is difficult to visualize and difficult to analyze. |
