Dichotomy of ergodic measures on linear spaces

1995 ◽  
Vol 58 (6) ◽  
pp. 1357-1359 ◽  
Author(s):  
S. G. Khaliullin
2018 ◽  
Vol 11 (4) ◽  
pp. 103-112
Author(s):  
Mahdi Iranmanesh ◽  
Maryam Saeedi Khojasteh

2012 ◽  
Vol 14 (2) ◽  
pp. 157
Author(s):  
Yanqiu WANG ◽  
Huaxin ZHAO
Keyword(s):  

Fractals ◽  
2007 ◽  
Vol 15 (01) ◽  
pp. 63-72 ◽  
Author(s):  
JÖRG NEUNHÄUSERER

We develop the dimension theory for a class of linear solenoids, which have a "fractal" attractor. We will find the dimension of the attractor, proof formulas for the dimension of ergodic measures on this attractor and discuss the question of whether there exists a measure of full dimension.


2021 ◽  
pp. 108985
Author(s):  
Chun-Kit Lai ◽  
Bochen Liu ◽  
Hal Prince

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 80
Author(s):  
Sergey Kryzhevich ◽  
Viktor Avrutin ◽  
Nikita Begun ◽  
Dmitrii Rachinskii ◽  
Khosro Tajbakhsh

We studied topological and metric properties of the so-called interval translation maps (ITMs). For these maps, we introduced the maximal invariant measure and demonstrated that an ITM, endowed with such a measure, is metrically conjugated to an interval exchange map (IEM). This allowed us to extend some properties of IEMs (e.g., an estimate of the number of ergodic measures and the minimality of the symbolic model) to ITMs. Further, we proved a version of the closing lemma and studied how the invariant measures depend on the parameters of the system. These results were illustrated by a simple example or a risk management model where interval translation maps appear naturally.


Author(s):  
Anna Bahyrycz ◽  
Justyna Sikorska

AbstractLet X, Y be linear spaces over a field $${\mathbb {K}}$$ K . Assume that $$f :X^2\rightarrow Y$$ f : X 2 → Y satisfies the general linear equation with respect to the first and with respect to the second variables, that is, for all $$x,x_i,y,y_i \in X$$ x , x i , y , y i ∈ X and with $$a_i,\,b_i \in {\mathbb {K}}{\setminus } \{0\}$$ a i , b i ∈ K \ { 0 } , $$A_i,\,B_i \in {\mathbb {K}}$$ A i , B i ∈ K ($$i \in \{1,2\}$$ i ∈ { 1 , 2 } ). It is easy to see that such a function satisfies the functional equation for all $$x_i,y_i \in X$$ x i , y i ∈ X ($$i \in \{1,2\}$$ i ∈ { 1 , 2 } ), where $$C_1:=A_1B_1$$ C 1 : = A 1 B 1 , $$C_2:=A_1B_2$$ C 2 : = A 1 B 2 , $$C_3:=A_2B_1$$ C 3 : = A 2 B 1 , $$C_4:=A_2B_2$$ C 4 : = A 2 B 2 . We describe the form of solutions and study relations between $$(*)$$ ( ∗ ) and $$(**)$$ ( ∗ ∗ ) .


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