Backward orbits of operators

Author(s):  
Vladimir Müller

2008 ◽  
Vol 89 (2) ◽  
pp. 145-173 ◽  
Author(s):  
Sergio Bermudo ◽  
Alfonso Montes-Rodríguez ◽  
Stanislav Shkarin


2012 ◽  
Vol 18 (7) ◽  
pp. 1193-1203 ◽  
Author(s):  
Peter Maličký
Keyword(s):  


2006 ◽  
Vol 318 (2) ◽  
pp. 459-466 ◽  
Author(s):  
Ralph deLaubenfels
Keyword(s):  


2020 ◽  
Vol 7 (1) ◽  
pp. 133-154
Author(s):  
V. Müller ◽  
Yu. Tomilov

AbstractWe present a survey of some recent results concerning joint numerical ranges of n-tuples of Hilbert space operators, accompanied with several new observations and remarks. Thereafter, numerical ranges techniques will be applied to various problems of operator theory. In particular, we discuss problems concerning orbits of operators, diagonals of operators and their tuples, and pinching problems. Lastly, motivated by known results on the numerical radius of a single operator, we examine whether, given bounded linear operators T1, . . ., Tn on a Hilbert space H, there exists a unit vector x ∈ H such that |〈Tjx, x〉| is “large” for all j = 1, . . . , n.



2015 ◽  
Vol 74 (2) ◽  
pp. 281-306
Author(s):  
Heybetkulu Mustafayev




2019 ◽  
Vol 147 (9) ◽  
pp. 3947-3954 ◽  
Author(s):  
Leandro Arosio ◽  
Lorenzo Guerini
Keyword(s):  


Physics Today ◽  
2021 ◽  
Vol 74 (5) ◽  
pp. 12-14
Author(s):  
Johanna L. Miller
Keyword(s):  


2019 ◽  
Vol 3 (1) ◽  
Author(s):  
Yi-Chiuan Chen

Abstract For a Denjoy homeomorphism $f$ of the circle $S$, we call a pair of distinct points of the $\omega$-limit set $\omega (\,f)$ whose forward and backward orbits converge together a gap, and call an orbit of gaps a hole. In this paper, we generalize the Sturmian system of Morse and Hedlund and show that the dynamics of any Denjoy minimal set of finite number of holes is conjugate to a generalized Sturmian system. Moreover, for any Denjoy homeomorphism $f$ having a finite number of holes and for any transitive orientation-preserving homeomorphism $f_1$ of the circle with the same rotation number $\rho (\,f_1)$ as $\rho (\,f)$, we construct a family $f_\varepsilon$ of Denjoy homeomorphisms of rotation number $\rho (\,f)$ containing $f$ such that $(\omega (\,f_\varepsilon ), f_\varepsilon )$ is conjugate to $(\omega (\,f), f)$ for $0<\varepsilon <\tilde{\varepsilon }<1$, but the number of holes changes at $\varepsilon =\tilde{\varepsilon }$, that $(\omega (\,f_\varepsilon ), f_\varepsilon )$ is conjugate to $(\omega (\,f_{\tilde{\varepsilon }}), f_{\tilde{\varepsilon }})$ for $\tilde{\varepsilon }\leqslant \varepsilon <1$ but $\lim _{\varepsilon \nearrow 1}f_\varepsilon (t)=f_1(t)$ for any $t\in S$, and that $f_\varepsilon$ has a singular limit when $\varepsilon \searrow 0$. We show this singular limit is an anti-integrable limit (AI-limit) in the sense of Aubry. That is, the Denjoy minimal system reduces to a symbolic dynamical system. The AI-limit can be degenerate or nondegenerate. All transitions can be precisely described in terms of the generalized Sturmian systems.





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