Temat: expanding map - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Most expanding maps have no absolutely continuous invariant measure
Autorzy:: Quas, Anthony N.
Powiązania:: https://bibliotekanauki.pl/articles/1217126.pdf
Data publikacji:: 1999
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: $C^1$ expanding map
Ruelle-Perron-Frobenius operator
Opis:: We consider the topological category of various subsets of the set of expanding maps from a manifold to itself, and show in particular that a generic $C^1$ expanding map of the circle has no absolutely continuous invariant probability measure. This is in contrast with the situation for $C^2$ or $C^{1+ε}$ expanding maps, for which it is known that there is always a unique absolutely continuous invariant probability measure.
Źródło:: Studia Mathematica; 1999, 134, 1; 69-78
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: More on linear and metric tree maps
Autorzy:: Kozerenko, Sergiy
Powiązania:: https://bibliotekanauki.pl/articles/1397335.pdf
Data publikacji:: 2021
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: Markov graph
metric map
non-expanding map
linear map
graph homomorphism
Opis:: We consider linear and metric self-maps on vertex sets of finite combinatorial trees. Linear maps are maps which preserve intervals between pairs of vertices whereas metric maps are maps which do not increase distances between pairs of vertices. We obtain criteria for a given linear or a metric map to be a positive (negative) under some orientation of the edges in a tree, we characterize trees which admit maps with Markov graphs being paths and prove that the converse of any partial functional digraph is isomorphic to a Markov graph for some suitable map on a tree.
Źródło:: Opuscula Mathematica; 2021, 41, 1; 55-70
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Distortion inequality for the Frobenius-Perron operator and some of its consequences in ergodic theory of Markov maps in $ℝ^d$
Autorzy:: Bugiel, Piotr
Powiązania:: https://bibliotekanauki.pl/articles/1294475.pdf
Data publikacji:: 1998
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: invariant measure
Frobenius-Perron operator
expanding map
distortion inequality
Opis:: Asymptotic properties of the sequences (a) ${P^j_φ g}_{j=1}^{∞}$ and (b) ${j^{-1} ∑_{i=0}^{j-1} Pⁱ_φ g}_{j=1}^{∞}$, where $P_φ:L¹ → L¹$ is the Frobenius-Perron operator associated with a nonsingular Markov map defined on a σ-finite measure space, are studied for g ∈ G = {f ∈ L¹: f ≥ 0 and ⃦f ⃦ = 1}. An operator-theoretic analogue of Rényi's Condition is introduced. It is proved that under some additional assumptions this condition implies the L¹-convergence of the sequences (a) and (b) to a unique g₀ ∈ G. The general result is applied to some smooth Markov maps in $ℝ^d$. Also the Bernoulli property is proved for a class of smooth Markov maps in $ℝ^d$.
Źródło:: Annales Polonici Mathematici; 1998, 68, 2; 125-157
0066-2216
Pojawia się w:: Annales Polonici Mathematici
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 4.

Tytuł:: Invariant densities for C¹ maps
Autorzy:: N. Quas, Anthony
Powiązania:: https://bibliotekanauki.pl/articles/1287383.pdf
Data publikacji:: 1996
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: cocycle
expanding map
invariant density
absolutely continuous invariant measure
Opis:: We consider the set of $C^1$ expanding maps of the circle which have a unique absolutely continuous invariant probability measure whose density is unbounded, and show that this set is dense in the space of $C^1$ expanding maps with the $C^1$ topology. This is in contrast with results for $C^2$ or $C^{1+ε}$ maps, where the invariant densities can be shown to be continuous.
Źródło:: Studia Mathematica; 1996, 120, 1; 83-88
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

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