An alternative canonical approach to the ghost problem in a complexified extension of the Pais-Uhlenbeck oscillator.
An analogue of the Variational Principle for group and pseudogroup actions
We generalize to the case of finitely generated groups of homeomorphisms the notion of a local measure entropy introduced by Brin and Katok [7] for a single map. We apply the theory of dimensional type characteristics of a dynamical system elaborated by Pesin [25] to obtain a relationship between the topological entropy of a pseudogroup and a group of homeomorphisms of a metric space, defined by Ghys, Langevin and Walczak in [12], and its local measure entropies. We prove an analogue of the Variational...
An analogue to the Smale-Birkhoff homoclinic theorem for iterated entire mappings. (Summary).
An analogue to the Smale-Birkhoff homoclinic theorem for iterated entire mappings.
An anti-classification theorem for ergodic measure preserving transformations
Despite many notable advances the general problem of classifying ergodic measure preserving transformations (MPT) has remained wide open. We show that the action of the whole group of MPT’s on ergodic actions by conjugation is turbulent in the sense of G. Hjorth. The type of classifications ruled out by this property include countable algebraic objects such as those that occur in the Halmos–von Neumann theorem classifying ergodic MPT’s with pure point spectrum. We treat both the classical case of...
An Application of Skew Product Maps to Markov Chains
By using the skew product definition of a Markov chain we obtain the following results: (a) Every k-step Markov chain is a quasi-Markovian process. (b) Every piecewise linear map with a Markovian partition defines a Markov chain for every absolutely continuous invariant measure. (c) Satisfying the Chapman-Kolmogorov equation is not sufficient for a process to be quasi-Markovian.
An application of the dual variational principle to a Hamiltonian system with discontinuous nonlinearities.
An application of the topological rigidity of the sine family.
An approach to robust control of the Hopf bifurcation.
An approach to zeta-function of finite factorgraph via the Markov topological chains
An arithmetic group associated with a Pisot unit, and its symbolic-dynamical representation
An attraction result and an index theorem for continuous flows on
We study the behavior of a continuous flow near a boundary. We prove that if φ is a flow on for which is an invariant set and S ⊂ ∂E is an isolated invariant set, with non-zero homological Conley index, then there exists an x in EE such that either α(x) or ω(x) is in S. We also prove an index theorem for a flow on .
An earthquake version of the Jackson-Zygmund theorem.
An elementary proof of a Lima's theorem for surfaces.
An elementary proof of the following theorem is given:THEOREM. Let M be a compact connected surface without boundary. Consider a C∞ action of Rn on M. Then, if the Euler-Poincaré characteristic of M is non zero there exists a fixed point.
An entropy for -actions with finite entropy generators
We study a definition of entropy for -actions (or -actions) due to S. Friedland. Unlike the more traditional definition, this is better suited for actions whose generators have finite entropy as single transformations. We compute its value in several examples. In particular, we settle a conjecture of Friedland [2].
An Epidemic Model With Post-Contact Prophylaxis of Distributed Length II. Stability and Oscillations if Treatment is Fully Effective
A possible control strategy against the spread of an infectious disease is the treatment with antimicrobials that are given prophylactically to those that had contact with an infective person. The treatment continues until recovery or until it becomes obvious that there was no infection in the first place. The model considers susceptible, treated uninfected exposed, treated infected, (untreated) infectious, and recovered individuals. The overly optimistic assumptions are made that treated uninfected...
An ergodic sum related to the approximation by continued fractions.
An example of a conservative exact endomorphism which is not lim sup full.
An example of a genuinely discontinuous generically chaotic transformation of the interval
It is proved that a piecewise monotone transformation of the unit interval (with a countable number of pieces) is generically chaotic. The Gauss map arising in connection with the continued fraction expansions of the reals is an example of such a transformation.
An example of infinitely many sinks for smooth interval maps.