On the trajectories of a particle in a translation invariant involutive field
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910387993051136 |
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| author | Cobeli, Cristian Zaharescu, Alexandru |
| author_facet | Cobeli, Cristian Zaharescu, Alexandru |
| contents | We introduce a double-folded operator that, upon iterative application, generates a dynamical system with two types of trajectories: a cyclic one and, another that grows endlessly on parabolas. These trajectories produce two distinct partitions of the set of lattice points in the plane.
Our object is to analyze these trajectories and to point out a few special arithmetic properties of the integers they represent.
We also introduce and study the parabolic-taxicab distance, which measures the fast traveling on the steps of the stairs defined by points on the parabolic trajectories whose coordinates are based on triangular numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_14894 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the trajectories of a particle in a translation invariant involutive field Cobeli, Cristian Zaharescu, Alexandru Number Theory Primary 11B37, Secondary 11B50 We introduce a double-folded operator that, upon iterative application, generates a dynamical system with two types of trajectories: a cyclic one and, another that grows endlessly on parabolas. These trajectories produce two distinct partitions of the set of lattice points in the plane. Our object is to analyze these trajectories and to point out a few special arithmetic properties of the integers they represent. We also introduce and study the parabolic-taxicab distance, which measures the fast traveling on the steps of the stairs defined by points on the parabolic trajectories whose coordinates are based on triangular numbers. |
| title | On the trajectories of a particle in a translation invariant involutive field |
| topic | Number Theory Primary 11B37, Secondary 11B50 |
| url | https://arxiv.org/abs/2403.14894 |