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Conjugacy of Maps

In: An Introduction to Dynamical Systems and Chaos

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  • G. c. Layek

    (The University of Burdwan, Department of Mathematics)

Abstract

The notion of topological conjugacy is very important in connecting the dynamics of different maps. It relates the properties among mapsMaps through some conjugacy. In other way, conjugacy is a change of variables that transforms one map into another. The variable changes from one system to another, that is, transition mappings are invertible and continuous, but not necessarily affine (a combination of linear transformation and translation). Two maps are said to be conjugate if they are equivalent to each other and their dynamics are similar. Conjugacy is an equivalence relation among maps. In conjugacy relation, the transformation should be a homeomorphism, so that some topological structures are preserved. Naturally, it is a useful and also a wise trick to find conjugacy between a map and an easier map.

Suggested Citation

  • G. c. Layek, 2015. "Conjugacy of Maps," Springer Books, in: An Introduction to Dynamical Systems and Chaos, chapter 0, pages 481-495, Springer.
    • Handle: RePEc:spr:sprchp:978-81-322-2556-0_11
    DOI: 10.1007/978-81-322-2556-0_11
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