Examples of conjugacy

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This is merely the definition of stable conjugacy class for strongly regular elements.
Conjugacy and rigidity for nonpositively curved manifolds of higher rank.
It is known that the two effect the same scaling of the frequencies of motions and therefore coincide up to conjugacy.
Any orientation-preserving conjugacy of two exponential maps induces an order-preserving map on their sets of escaping points.
Furthermore, the isometry between two foliations is equivalent to the conjugacy between the dihedral group actions on the covering spaces [10].
Stable conjugacy is a slight variant of this using the stable centralizer.
If we require (0) = 0, then the conjugacy is unique.
If the conjugacy is also analytic, the map f is said to be analytically linearizable.
Comparing these invariants for different shape parameters then gives necessary conditions for conjugacy.
The next theorem gives an analytic conjugacy in a jet class.
Lastly, we study the interplay between change of metric and dynamics, for which purpose we consider isometric conjugacy.
The most useful notion of 'modelling' is that of topological conjugacy.
Nevertheless, this conjugacy does not really depend on the particular choice of the stationary measure.
This leads to the result that the conjugacy considered here is essentially one-sided.
The subcollections nest down as smoothness increases, and by rigidity these smoothness classes are also conjugacy classes.
The conjugacy is then uniquely defined from the conjugacy equation by the dynamics.
One immediately checks that with this definition is a conjugacy.
In our context, rigidity means that, for some systems, data at periodic orbits determine the smooth conjugacy class.
In each case a measurable conjugacy is constructed, but the map is only continuous after exclusion of certain sets of measure zero.

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