Zobrazeno 1 - 10
of 55
pro vyhledávání: '"Bakhtin, V. I."'
Autor:
Bakhtin, V. I.
It is proved that a parameterized curve in a metric space $X$ is absolutely continuous if and only if its composition with any Lipschitz function on $X$ is absolutely continuous.
Comment: 7 pages
Comment: 7 pages
Externí odkaz:
http://arxiv.org/abs/2406.08941
Autor:
Bakhtin, V. I.
An ergodic support $X_0$ of a dynamical system $(X,T)$ with metrizable compact phase space $X$ is the set of all points $x\in X$ such that the corresponding sequence of empirical measures $\delta_{x,n} = (\delta_x +\delta_{Tx}+\dots +\delta_{T^{n-1}x
Externí odkaz:
http://arxiv.org/abs/2309.10573
Autor:
Bakhtin, V. I., Lebedev, A. V.
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 characteristics of information theory and thermodynamic formalism (entropy a
Externí odkaz:
http://arxiv.org/abs/2107.02166
Sup-sums principles for F-divergence, Kullback--Leibler divergence, and new definition for t-entropy
Autor:
Bakhtin, V. I., Lebedev, A. V.
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. As applications of these results we derive the corresponding sup-sums
Externí odkaz:
http://arxiv.org/abs/1909.06597
Autor:
Bakhtin, V. I., Lebedev, A. V.
For any transfer operator we establish the equivalence of variational principles for $t$-entropy, the spectral potential and entropy statistic theorem and give new proofs for all these statements.
Comment: 10 pages. arXiv admin note: text overla
Comment: 10 pages. arXiv admin note: text overla
Externí odkaz:
http://arxiv.org/abs/1707.01431
Autor:
Bakhtin, V. I., Lebedev, A. V.
New direct proofs of variational principles for $t$-entropy, spectral radius of weighted shift operators, and entropy statistic theorem are given. The equivalence of these statements is obtained.
Comment: 11 pages
Comment: 11 pages
Externí odkaz:
http://arxiv.org/abs/1705.01270
Autor:
Bakhtin, V. I.
For simplest colored branching processes we prove an analog to the McMillan theorem and calculate Hausdorff dimensions of random fractals defined in terms of the limit behavior of empirical measures generated by finite genetic lines. In this setting
Externí odkaz:
http://arxiv.org/abs/1211.7270
Autor:
Bakhtin, V. I., Lebedev, A. V.
The article presents a new definition of t-entropy that makes it more explicit and simplifies the process of its calculation.
Comment: 8 pages
Comment: 8 pages
Externí odkaz:
http://arxiv.org/abs/0906.4969
T-entropy and Variational Principle for the spectral radius of transfer and weighted shift operators
Publikováno v:
Ergod. Th. & Dynam. Sys. (2011) V. 31. P. 995--1042
The paper deals with the variational principles for evaluation of the spectral radii of transfer and weighted shift operators associated with a dynamical system. These variational principles have been the matter of numerous investigations and the pri
Externí odkaz:
http://arxiv.org/abs/0809.3116
Autor:
Bakhtin, V. I.
Publikováno v:
Ergod. Th. & Dynam. Sys. (2010) V. 30. P. 1331--1342
In this paper we introduce a new functional invariant of discrete time dynamical systems -- the so-called t-entropy. The main result is that this t-entropy is the Legendre dual functional to the logarithm of the spectral radius of the weighted shift
Externí odkaz:
http://arxiv.org/abs/0809.3106