Richness of Hamiltonian chaos

Since the time of Newton, physicists have described natural processes through differential equations. Nowadays it is commonly acknowledged that solutions to differential equations are often chaotic: a small variation in initial conditions leads to a large and unpredictable change in the behavior of the system. One should, therefore, try to describe this behavior statistically. However, we will show that a system with chaotic behavior often exhibits a variety of statistical patterns of such diversity that any attempt to comprehensively describe it will fail. We will argue that this ultimate richness is the main characteristic feature of chaos in practically any given system and show how this fact could help explain otherwise unexplained
physical phenomena, like the low temperature flicker-noise in metals.