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1
Content available remote

A method of construction of an invariant measure

100%
Dawidowicz A.
Annales Polonici Mathematici
|
1992
|
tom 57
|
nr 3
205-208
EN
A method of construction of an invariant measure on a function space is presented.
2
Content available remote

The stability study of a plane engine

100%
Kołodziej R., Nowicki T.
Applicationes Mathematicae
|
2000
|
tom 27
|
nr 1
35-44
EN
We study the dynamical properties of a plane engine vibrations modelled by a system of ODE.
3
Content available remote

Stability of Markov processes nonhomogeneous in time

80%
Tyran-Kamińska M.
Annales Polonici Mathematici
|
1999
|
tom 71
|
nr 1
47-59
EN
We study the asymptotic behaviour of discrete time processes which are products of time dependent transformations defined on a complete metric space. Our sufficient condition is applied to products of Markov operators corresponding to stochastically perturbed dynamical systems and fractals.
4
Content available remote

A note on generic chaos

80%
Liao G.
Annales Polonici Mathematici
|
1994
|
tom 59
|
nr 2
99-105
EN
We consider dynamical systems on a separable metric space containing at least two points. It is proved that weak topological mixing implies generic chaos, but the converse is false. As an application, some results of Piórek are simply reproved.
5
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Dynamical systems with multiplicative perturbations: the strong convergence of measures

80%
Horbacz K.
Annales Polonici Mathematici
|
1993
|
tom 58
|
nr 1
85-93
EN
We give sufficient conditions for the strong asymptotic stability of the distributions of dynamical systems with multiplicative perturbations. We apply our results to iterated function systems.
6
Content available remote

Time to the convergence of evolution in the space of population states

80%
Karcz-Dulęba I.
International Journal of Applied Mathematics and Computer Science
|
2004
|
tom 14
|
nr 3
279-287
EN
Phenotypic evolution of two-element populations with proportional selection and normally distributed mutation is considered. Trajectories of the expected location of the population in the space of population states are investigated. The expected location of the population generates a discrete dynamical system. The study of its fixed points, their stability and time to convergence is presented. Fixed points are located in the vicinity of optima and saddles. For large values of the standard deviation of mutation, fixed points become unstable and periodical orbits arise. In this case, fixed points are also moved away from optima. The time to convergence to fixed points depends not only on the mutation rate, but also on the distance of the points from unstability. Results show that a population spends most time wandering slowly towards the optimum with mutation as the main evolution factor.
7
Content available remote

Topological entropy on zero-dimensional spaces

80%
Bobok J., Zindulka O.
Fundamenta Mathematicae
|
1999
|
tom 162
|
nr 3
233-249
EN
Let X be an uncountable compact metrizable space of topological dimension zero. Given any a ∈[0,∞] there is a homeomorphism on X whose topological entropy is a.
8
Content available remote

Propriétés topologiques et combinatoires des échelles de numération

70%
Barat G., Downarowicz T., Iwanik A., Liardet P.
Colloquium Mathematicum
|
2000
|
tom 84/85
|
nr 2
285-306
EN
Topological and combinatorial properties of dynamical systems called odometers and arising from number systems are investigated. First, a topological classification is obtained. Then a rooted tree describing the carries in the addition of 1 is introduced and extensively studied. It yields a description of points of discontinuity and a notion of low scale, which is helpful in producing examples of what the dynamics of an odometer can look like. Density of the orbits is also discussed.
9
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Co możemy opisać układem dynamicznym?

61%
Foryś U.
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
|
2014
|
tom 6
73-85
PL
In this paper we present several examples of simple dynamical systemsdescribing various real processes. We start from well know Fibonaccisequence, through Lotka-Volterra model of prey-predator system, love affairdynamics, ending with modelling of tumour growth.
10
Content available remote

Modulating element method in the identification of a generalized dynamical system

61%
Wysocki H., Zellma M.
Applicationes Mathematicae
|
1993-1995
|
tom 22
|
nr 4
447-467
EN
In this paper the identification of generalized linear dynamical differential systems by the method of modulating elements is presented. The dynamical system is described in the Bittner operational calculus by an abstract linear differential equation with constant coefficients. The presented general method can be used in the identification of stationary continuous dynamical systems with compensating parameters and for certain nonstationary compensating or distributed parameter systems.
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