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.
An existence result on periodic solutions of an ordinary -Laplacian system.
An exotic flow on a compact surface
In 1988 Anosov [1] published the construction of an example of a flow (continuous real action) on a cylinder or annulus with a phase portrait strikingly different from our normal experience. It contains orbits whose -limit sets contain a non-periodic orbit along with a simple closed curve of fixed points, but these orbits do not wrap down on this simple closed curve in the usual way. In this paper we modify some of Anosov’s methods to construct a flow on a surface of genus with equally striking...
An explicit formula for symmetric polynomials related to the eigenfunctions of Calogero-Sutherland models.
An explicit separate solution for the Tzitzeica equation.
An exponential estimate for convolution powers
We establish an exponential estimate for the relationship between the ergodic maximal function and the maximal operator associated with convolution powers of a probability measure.
An extension of Markov partitions for a certain toral endomorphism.
An extension of the Artin-Mazur theorem.