Abstract
We study the behaviour of trajectories of real homeomorphisms h. There are exactly 15 order types among them. For each h let \(T_h\) be the collection of all order types of h-trajectories. This \(T_h\) will be called a package (of order types). We prove that \( \mid T_h\mid \le 11\) always. As h varies over the set of all homeomorphisms from \({\mathbb {R}}\) to \({\mathbb {R}}\), we ask how many sets can arise as \(T_h\)? We prove that the answer is exactly 36. An example is given at the end to show how these packages are helpful for conjugacy classification.
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Acknowledgements
The second author acknowledges the Council of Scientific & Industrial Research, India, for financial support (Ref. No. 09/1045(0042)/2020-EMR-I).
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Communicated by S.G. Dani.
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Kannan, V., Malegaonkar, S. 15 Order types in 36 packages. Indian J Pure Appl Math (2024). https://doi.org/10.1007/s13226-024-00538-y
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DOI: https://doi.org/10.1007/s13226-024-00538-y