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Examples ofparabolic point
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Since f has noparabolicpoint, horocyclicity is trivial.
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Here we should be careful about the boundary correspondence near the preimages of aparabolicpointwhich is perturbed into an attracting planet.
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Since is finite we may fix > 0 good for all parabolic points.
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Our first result about condensation of at parabolic points is the following.
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For this we first give some estimates for the measure on certain fundamental cells associated with the stabilizers of the parabolic points.
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In other words, critical points increase the chances of various points (particularly parabolic points) to be of infinite condensation.
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The next section, 5 is devoted to the study of points of infinite condensation of and 6, its natural continuation, deals with parabolic points.
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By modifying this metric near the parabolic points, we have the following.
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For our purposes it is sufficient to investigate the behaviour of around each of the parabolic points.
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Here we introduce the notion of planets and satellites for periodic points generated by the perturbation of parabolic points.
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We also show that such cumulated effect gives rise to a weaker sufficient requirement for parabolic points to be of infinite condensation.
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In the case of surfaces in 3-space, the non-degenerate surfaces are those without parabolic points.
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This example is from Wikipedia and may be reused under a CC BY-SA license.These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.