24 citations · 60 across the 13 of their papers we have counts for
14 papers
Convexity and concavity of -potentials (Kolmogorov means)
V. I. Bakhtin, N. A. Tsarev
In the paper we prove criteria for convexity and concavity of -potentials (-means, Kolmogorov means, weighted quasi-arithmetic means), which particular cases are the arithmet…
Criterion for the absolute continuity of curves in metric spaces
V. I. Bakhtin
It is proved that a parameterized curve in a metric space is absolutely continuous if and only if its composition with any Lipschitz function on is absolutely continuous.
An ergodic support of a dynamical system and a natural representation of Choquet distributions for invariant measures
V. I. Bakhtin
An ergodic support of a dynamical system with metrizable compact phase space is the set of all points such that the corresponding sequence of empirical m…
Analysis of relationships between spectral potential of transfer operators, -entropy, entropy and topological pressure
V. I. Bakhtin, A. V. Lebedev
The paper is devoted to the analysis of relationships between principal objects of the spectral theory of dynamical systems (transfer and weighted shift operators) and basic charac…
Sup-sums principles for F-divergence, Kullback--Leibler divergence, and new definition for t-entropy
V. I. Bakhtin, A. V. Lebedev
The article presents new sup-sums principles for integral F-divergence for arbitrary convex function F and arbitrary (not necessarily positive and absolutely continuous) measures.…
Variational principles for t-entropy, the spectral potential of transfer operator, and entropy statistic theorem are equivalent
V. I. Bakhtin, A. V. Lebedev
For any transfer operator we establish the equivalence of variational principles for -entropy, the spectral potential and entropy statistic theorem and give new proofs for all t…