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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-partial… Expand
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 and… Expand
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 four… Expand
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 for… Expand
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 assume… Expand
Bounds for periodic solutions of differential equations in Banach spaces
A NEW APPROACH TO THE DEFINITION ON TOPOLOGICAL DEGREE FOR MULTI-VALUED MAPPINGS.
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, locally… Expand
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 x… Expand