Genericity in Topological Dynamics

We study genericity of dynamical properties in the space of homeomorphisms of the Cantor set and in the space of subshifts of a suitably large shift space. These rather different settings are related by a Glasner-King type correspondence: genericity in one is equivalent to genericity in the other. By applying symbolic techniques in the shift-space model we derive new results about genericity of dynamical properties for transitive and totally transitive homeomorphisms of the Cantor set. We show that the isomorphism class of the universal odometer is generic in the space of transitive systems. On the other hand, the space of totally transitive systems displays much more varied dynamics. In particular, we show that in this space the isomorphism class of every Cantor system without periodic points is dense, and the following properties are generic: minimality, zero entropy, disjointness from a fixed totally transitive system, weak mixing, strong mixing, and minimal self joinings. The last two stand in striking contrast to the situation in the measure-preserving category. We also prove a correspondence between genericity of dynamical properties in the measure-preserving category and genericity of systems supporting an invariant measure with the same property.Comment: 48 pages, to appear in Ergodic Theory Dynamical Systems. v2: revised exposition, added proof that the universal odometer is generic among transitive Cantor homeomorphism

MezÅ‘gazdasági fedezeti ügyletek és piaci hatékonyságuk a Budapesti ÉrtéktÅ‘zsdén

A mezÅ‘gazdasági vállalkozásokban jelentÅ‘s kockázat az árkockázat. Fedezeti ügyletekkel aktív kockázatkezelést folytató gazdálkodók száma jelentÅ‘sen elmarad a nemzetközi átlagtól. Az árutÅ‘zsde hatékony működése szükséges ahhoz, hogy megfelelÅ‘ határidÅ‘s ügyletekkel az árkockázat eliminálható legyen. A hatékonysági vizsgálatok igazolták a gyenge szintű tÅ‘kepiaci hatékonyság meglétét, így a hazai határidÅ‘s piac ebbÅ‘l a szempontból alkalmas a hatékony kockázatmenedzsmentre. Ugyanakkor a hatékonyság rendre elmarad a fejlettebb azonnali részvénypiaci szekciótól. A piaci likviditás és párhuzamosan a piaci hatékonyság jelentÅ‘sen növelhetÅ‘ lenne, amennyiben a mezÅ‘gazdasági vállalkozások megismernék, megértenék a határidÅ‘s piacokban lévÅ‘ kockázatmérséklési lehetÅ‘ségeket. ----------------------------------------------------------- The second highest risk factor for agricultural enterprises is the price risk. Hedge transactions for agricultural risk management remarkably less used than in Western Europe or in the USA. Efficient operation of the commodity exchange is essential for eliminating price risk. The results confirm the weak form of the market efficiency, which means that – from this point of view – the market is applicable to the eligible risk management, albeit the level of efficiency is lower than the more developed equity exchange. The liquidity and the efficiency of the market could be improved by agricultural enterprises which are aware of and capable of using ways to mitigate risks.fedezeti ügylet, hatékonyság, árutÅ‘zsde, kockázatkezelés, hedge transaction, market efficiency, produce exchange, agricultural risk management, market liquidity, Agricultural Finance, Financial Economics,

On the polar decomposition of right linear operators in quaternionic Hilbert spaces

In this article we prove the existence of the polar decomposition for densely defined closed right linear operators in quaternionic Hilbert spaces: If $T$ is a densely defined closed right linear operator in a quaternionic Hilbert space $H$, then there exists a partial isometry $U_{0}$ such that $T = U_{0}|T|$. In fact $U_{0}$ is unique if $N(U_{0}) = N(T)$. In particular, if $H$ is separable and $U$ is a partial isometry with $T = U|T|$, then we prove that $U = U_{0}$ if and only if either $N(T) = \{0\}$ or $R(T)^{\bot} = \{0\}$.Comment: 17 page

Fundamental domain of invariant sets and applications

Let $X$ be a compact metric space and $f:X\to X$ a homeomorphism on $X$. We construct a fundamental domain for the set with finite peaks for each cocycle induced by $\phi\in C(X,R)$. In particular we prove that if a partially hyperbolic diffeomorphism is accessible, then either the set with finite peaks for the Jacobian cocycle is of full volume, or the set of transitive points is of positive volume

Fuzzy Bigraphs: An Exercise in Fuzzy Communicating Agents

Bigraphs and their algebra is a model of concurrency. Fuzzy bigraphs are a generalization of birgraphs intended to be a model of concurrency that incorporates vagueness. More specifically, this model assumes that agents are similar, communication is not perfect, and, in general, everything is or happens to some degree.Comment: 11 pages, 3 figure