Matches in SemOpenAlex for { <https://semopenalex.org/work/W2083703957> ?p ?o ?g. }
Showing items 1 to 65 of
65
with 100 items per page.
- W2083703957 endingPage "2421" @default.
- W2083703957 startingPage "2403" @default.
- W2083703957 abstract "This paper studies the relationship between the return time $tau_n$ and the Rényi Entropy Function of order $s$, $R(s)$. For a dynamical system with an invariant $alpha$-mixing measure $mu$ and a measurable partition, we consider the sum $W$ of measures of cylinders along orbit segments of length $tau_n$ and relate that growth/decay rate to the R$acute{textrm{e}}$nyi Entropy. The key strategy is to introduce the hitting number $nu_x(A) = | {1 leq i leq tau_n(x) : T^i(x) in A}|$, the number of times that $x$ hits the set $A$ when $x$ travels along its orbit of length $tau_n(x)$, and write $W=sum nu_x(A) mu(A)^s$, where the sum is taken over the $n$-cylinders. Then we show that $nu_x(A) approx exp(n h_{mu}) mu(A)$ for most $n$-cylinders $A$. Hence $W approx exp(nh_{mu}) sum mu(A)^{1+s}$, which relates $tau_n(x)$ to $R(s)$, as the sum $sum mu(A)^{1+s} approx exp(-nsR(s))$." @default.
- W2083703957 created "2016-06-24" @default.
- W2083703957 creator A5009382898 @default.
- W2083703957 date "2013-01-01" @default.
- W2083703957 modified "2023-10-05" @default.
- W2083703957 title "Rényi entropy and recurrence" @default.
- W2083703957 cites W1498335665 @default.
- W2083703957 cites W1635286099 @default.
- W2083703957 cites W1979818757 @default.
- W2083703957 cites W2013122593 @default.
- W2083703957 cites W2055390006 @default.
- W2083703957 cites W2122882636 @default.
- W2083703957 cites W2130509588 @default.
- W2083703957 cites W2133399915 @default.
- W2083703957 cites W2152755776 @default.
- W2083703957 doi "https://doi.org/10.3934/dcds.2013.33.2403" @default.
- W2083703957 hasPublicationYear "2013" @default.
- W2083703957 type Work @default.
- W2083703957 sameAs 2083703957 @default.
- W2083703957 citedByCount "3" @default.
- W2083703957 countsByYear W20837039572013 @default.
- W2083703957 countsByYear W20837039572015 @default.
- W2083703957 crossrefType "journal-article" @default.
- W2083703957 hasAuthorship W2083703957A5009382898 @default.
- W2083703957 hasConcept C10138342 @default.
- W2083703957 hasConcept C111919701 @default.
- W2083703957 hasConcept C114614502 @default.
- W2083703957 hasConcept C121332964 @default.
- W2083703957 hasConcept C162324750 @default.
- W2083703957 hasConcept C182306322 @default.
- W2083703957 hasConcept C2777894999 @default.
- W2083703957 hasConcept C33923547 @default.
- W2083703957 hasConcept C37914503 @default.
- W2083703957 hasConcept C41008148 @default.
- W2083703957 hasConceptScore W2083703957C10138342 @default.
- W2083703957 hasConceptScore W2083703957C111919701 @default.
- W2083703957 hasConceptScore W2083703957C114614502 @default.
- W2083703957 hasConceptScore W2083703957C121332964 @default.
- W2083703957 hasConceptScore W2083703957C162324750 @default.
- W2083703957 hasConceptScore W2083703957C182306322 @default.
- W2083703957 hasConceptScore W2083703957C2777894999 @default.
- W2083703957 hasConceptScore W2083703957C33923547 @default.
- W2083703957 hasConceptScore W2083703957C37914503 @default.
- W2083703957 hasConceptScore W2083703957C41008148 @default.
- W2083703957 hasIssue "6" @default.
- W2083703957 hasLocation W20837039571 @default.
- W2083703957 hasOpenAccess W2083703957 @default.
- W2083703957 hasPrimaryLocation W20837039571 @default.
- W2083703957 hasRelatedWork W1522602455 @default.
- W2083703957 hasRelatedWork W1970092082 @default.
- W2083703957 hasRelatedWork W1975860297 @default.
- W2083703957 hasRelatedWork W2026168617 @default.
- W2083703957 hasRelatedWork W2043930649 @default.
- W2083703957 hasRelatedWork W2084143801 @default.
- W2083703957 hasRelatedWork W2949338451 @default.
- W2083703957 hasRelatedWork W3102427995 @default.
- W2083703957 hasRelatedWork W4226210834 @default.
- W2083703957 hasRelatedWork W4301484659 @default.
- W2083703957 hasVolume "33" @default.
- W2083703957 isParatext "false" @default.
- W2083703957 isRetracted "false" @default.
- W2083703957 magId "2083703957" @default.
- W2083703957 workType "article" @default.