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Let α be an action of Z d by continuous automorphisms of a compact abelian group X. A point x in X is called homoclinic for α if α n x → 0X as n → ∞. We study the set ∆α(X) of homoclinic points for α, which is a subgroup of X. If α is expansive then ∆α(X) is at most countable. Our main results are that if α is expansive, then (1) ∆α(x) is nontrivial if and(More)
We show that for certain classes of actions of Z d ; d 2, by automorphisms of the torus any measurable conjugacy has to be aane, hence measurable conjugacy implies algebraic conju-gacy; similarly any measurable factor is algebraic, and algebraic and aane centralizers provide invariants of measurable conjugacy. Using the algebraic machinery of dual modules(More)
Let α be an expansive automorphisms of compact connected abelian group X whose dual groupˆX is cyclic w.r.t. α (i.e. ˆ X is generated by {χ · α n : n ∈ Z} for some χ ∈ ˆ X). Then there exists a canonical group homomorphism ξ from the space ∞ (Z, Z) of all bounded two-sided sequences of integers onto X such that ξ · σ = α · ξ, where σ is the shift on ∞ (Z,(More)
We prove that certain Gibbs measures on subshifts of finite type are nonsingular and ergodic for certain countable equivalence relations, including the orbit relation of the adic transformation (the same as equality after a permutation of finitely many coordinates). The relations we consider are defined by cocycles taking values in groups, including some(More)
In this paper, we introduce the idea of abstraction-based diagnosability for large-scale composed discrete event systems that consist of multiple subsystems. To this end, we determine sufficient conditions such that diagnosability of the original system follows from diagnosability of an abstracted system model on a smaller state space. In addition, we prove(More)
Let d ≥ 1, and let α be an expansive Z d-action by continuous automorphisms of a compact abelian group X with completely positive entropy. Then the group ∆α(X) of homoclinic points of α is countable and dense in X, and the restriction of α to the α-invariant subgroup ∆α(X) is a Z d-action by automorphisms of ∆α(X). By duality, there exists a Z d-action α *(More)
In this paper, we investigate the verification of codiagnosability for discrete event systems (DES). That is, it is desired to ascertain if the occurrence of system faults can be detected based on the information of multiple local sites that partially observe the overall DES. As an improvement of existing codiagnosability tests that resort to the original(More)
—The FlexRay communication protocol is expected to be the de-facto standard for high-speed in-vehicle communication. In this paper, we formally investigate the scheduling problem for the dynamic segment of FlexRay. We take the bounds on the generation times and the timing requirements of the signals into consideration to propose a reservation based(More)