Abstract
A topological dynamical system is given by a topological space X and a transformation T: X → X. We will study the case where X is a metric space and T satisfies certain compatibility conditions with the topology, for example that T is continuous or Borel. The sequence x, T(x), T(T(x)), … of iterates of a point x ∈ X forms the trajectory or orbit of the point x.
All truly wise thoughts have been thought already thousands of times; but to make them truly ours, we must think them over again honestly, until they take root in our personal experience. J. W. von Goethe (1749–1832)
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Dudley, R.M.: Real Analysis and Probability. Cambridge Studies in Advanced Mathematics, vol. 74. Cambridge University Press, Cambridge (1989)
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© 2016 Springer-Verlag London
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Coudène, Y. (2016). Topological Dynamics. In: Ergodic Theory and Dynamical Systems. Universitext. Springer, London. https://doi.org/10.1007/978-1-4471-7287-1_5
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DOI: https://doi.org/10.1007/978-1-4471-7287-1_5
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