TL;DR
This paper proves the ergodic hypothesis for a specific class of functions in an infinite-dimensional setting without requiring metric transitivity, highlighting a unique result not applicable in finite dimensions.
Contribution
It establishes the ergodic hypothesis for a new class of functions in infinite-dimensional spaces without the usual metric transitivity condition.
Findings
Proves ergodic hypothesis in infinite-dimensional space
No finite analog of the result exists
Extends understanding of ergodic properties in complex spaces
Abstract
In this paper The Ergodic Hypothesis is proven for one class of functions defined in the infinite dimensional unite cube where is given an action of some semigroup of mappings without the condition on metric transitivity. The result has not a finite analog.
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Taxonomy
TopicsFunctional Equations Stability Results · Mathematical Dynamics and Fractals · Advanced Topology and Set Theory