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Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics
This is a treatment of a variety of mathematical systems generating densities, ranging from one-dimensional discrete time transformations through continuous time systems described by integro-partialExpand
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Chaos, Fractals, and Noise
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Probabilistic Properties of Deterministic Systems
1. Introduction 2. The toolbox 3. Markov and Frobenius-Perron operators 4. Studying chaos with densities 5. The asymptotic properties of densities 6. The behaviour of transformations on intervals andExpand
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Mathematical problems of the dynamics of the red blood cells
The purpose of this paper is to construct a model for the process of generation and degeneration of red blood cells, taking into account biological-medical experimental data. The paper contains fourExpand
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Globally asymptotic properties of proliferating cell populations
This paper presents a general model for the cell division cycle in a population of cells. Three hypotheses are used: (1) There is a substance (mitogen) produced by cells which is necessary forExpand
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Exact dynamical systems and the Frobenius-Perron operator
Conditions are investigated which guarantee exactness for measurable maps on measure spaces. The main application is to certain piecewise continuous maps T on [0,1] for which 7"(0) > 1. We assumeExpand
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Abstract : Multivalued mappings have become increasingly important in recent years in the mathematical theory of optimal control. In this paper, a certain approximation theorem on metric, locallyExpand
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A discrete boundary value problem
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The generic property of existence of solutions of differential equations in Banach space
where f: 77 --P E is continuous. A solution z(*) of (I) will be said to be a solution through us = (to , x0) if (2) is satisfied. Examples of continuous f are known for which there is no solution xExpand
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