Abstract
Schmeling introduced the concept of time weighted entropy in 2000 as a generalization of Pesin’s topological entropy. Since the potential function $$\phi $$ in topological pressure plays an important role in multifractal analysis and smooth ergodic theory, by analogy, we propose time weighted pressures. It is proved that time weighted pressures are generally different on non-invariant sets, and their properties concerning on the time complexity (with respect to the potential function $$\phi $$) of systems are explored. Further, it is shown that for a $$C^{1+\alpha }$$-diffeomorphism with a finite Markov partition, the corresponding coding map preserves time weighted pressures.
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