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- Subjects
- 37-XX Dynamical systems and ergodic theory
We determine, for certain ergodic infinite measure preserving transformations T, the asymptotic behaviour of the distribution of the waiting time for an excursion (from some fixed reference set of finite measure) of length larger than l as l → ∞, generalizing a renewal-theoretic result of Lamperti. This abstract distributional limit theorem applies to certain weakly expanding interval maps, where it clarifies the distributional behaviour of hitting times of shrinking neighbourhoods of neutral fixed...
The challenges to live in the open water and the diversity of habitats in the marine environments
prompts phytoplankton to devise strategies which often involve production of toxins
by Harmful Algal Bloom (HAB) and rapid production of metabolites from non-toxic precursor.
The functional response of the predator is described by Holling type IV. We investigate wave phenomena
and non-linear non-equilibrium pattern formation in a phytoplankton-zooplankton system
with Holling type IV functional response....
It is well known that a weakly almost periodic operator T in a Banach space is mean ergodic, and in the complex case, also λT is mean ergodic for every |λ|=1. We prove that a positive contraction on is weakly almost periodic if (and only if) it is mean ergodic. An example shows that without positivity the result is false. In order to construct a contraction T on a complex such that λT is mean ergodic whenever |λ|=1, but T is not weakly almost periodic, we prove the following: Let τ be an invertible...
We construct an example of a Morse ℤ²-action which has rank one and whose centralizer contains elements which cannot be weakly approximated by the transformations of the action.
We define by simple conditions two wide subclasses of the so-called Arnoux-Rauzy systems; the elements of the first one share the property of (measure-theoretic) weak mixing, thus we generalize and improve a counter-example to the conjecture that these systems are codings of rotations; those of the second one have eigenvalues, which was known hitherto only for a very small set of examples.
In this article we study the structure of the set of weakly product recurrent points. Among others, we provide necessary conditions (related to topological weak mixing) which imply that the set of weakly product recurrent points is residual. Additionally, some new results about the class of systems disjoint from every minimal system are obtained.
We construct a class of transformations similar to the Pascal transformation, except for the use of spacers, and show that these transformations are weakly mixing.
In 2005, İ. Tok fuzzified the notion of the topological entropy R. A. Adler et al. (1965) using the notion of fuzzy compactness of C. L. Chang (1968). In the present paper, we have proposed a new definition of the fuzzy topological entropy of fuzzy continuous mapping, namely weakly fuzzy topological entropy based on the notion of weak fuzzy compactness due to R. Lowen (1976) along with its several properties. We have shown that the topological entropy R. A. Adler et al. (1965) of continuous mapping...
Let (f,α) be the process given by an endomorphism f and by a finite partition of a Lebesgue space. Let E(f,α) be the class of densities of absolutely continuous invariant measures for skew products with the base (f,α). We say that (f,α) is quasi-Markovian if . We show that there exists a quasi-Markovian process which is weakly mixing but not mixing. As a by-product we deduce that the set of all coboundaries which are measurable with respect to the ’chequer-wise’ partition for σ × S, where σ is...
Utilizing the cut-and-stack techniques we construct explicitly a weakly mixing rigid rank-one transformation T which is conjugate to T². Moreover, it is proved that for each odd q, there is such a T commuting with a transformation of order q. For any n, we show the existence of a weakly mixing T conjugate to T² and whose rank is finite and greater than n.
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