Complexities of differentiable dynamical systems
Copyright policy )Complexities of differentiable dynamical systems
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.
Orbit growth in dynamical systems, ergodic theory, [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], Dynamical Systems (math.DS), Generic properties, structural stability of dynamical systems, dynamical systems, metric entropy, measure theory, Statistical thermodynamics, FOS: Mathematics, metric geometry, statistical thermodynamics, Entropy and other invariants, isomorphism, classification in ergodic theory, differential geometry, Mathematics - Dynamical Systems, Lyapunov exponent
Orbit growth in dynamical systems, ergodic theory, [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], Dynamical Systems (math.DS), Generic properties, structural stability of dynamical systems, dynamical systems, metric entropy, measure theory, Statistical thermodynamics, FOS: Mathematics, metric geometry, statistical thermodynamics, Entropy and other invariants, isomorphism, classification in ergodic theory, differential geometry, Mathematics - Dynamical Systems, Lyapunov exponent
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