Complexities of differentiable dynamical systems

Abstract

We define the notion of localizable property for a dynamical system. Then we survey three properties of complexity and relate how they are known to be typical among differentiable dynamical systems. These notions are the fast growth of the number of periodic points, the positive entropy and the high emergence. We finally propose a dictionary between the previously explained theory on entropy and the ongoing one on emergence.

References in corpus (6)

• Polynomial diffeomorphisms of C^2, IV: The measure of maximal entropy and laminar currents
• Generic Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits
• Measure concentration and the weak Pinsker property
• A generalization of Hausdorff dimension applied to Hilbert cubes and Wasserstein spaces
• Growth of the number of periodic points for meromorphic maps
• Abundance of fast growth of the number of periodic points in 2-dimensional area-preserving dynamics

Cited by in corpus (2)

• Emergence via non-existence of averages
• Highly irregular orbits for subshifts of finite type: large intersections and emergence