Castellani, Agnese
(2022)

*Automatic classification of stellar orbits in axisymmetric potentials.*
[Laurea magistrale], Università di Bologna, Corso di Studio in

Astrofisica e cosmologia [LM-DM270], Documento full-text non disponibile

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## Abstract

Within the classification of orbits in axisymmetric stellar systems, we present a new algorithm able to automatically classify the orbits according to their nature. The algorithm involves the application of the correlation integral method to the surface of section of the orbit; fitting the cumulative distribution function built with the consequents in the surface of section of the orbit, we can obtain the value of its logarithmic slope m which is directly related to the orbit’s nature: for slopes m ≈ 1 we expect the orbit to be regular, for slopes m ≈ 2 we expect it to be chaotic. With this method we have a fast and reliable way to classify orbits and, furthermore, we provide an analytical expression of the probability that an orbit is regular or chaotic given the logarithmic slope m of its correlation integral. Although this method works statistically well, the underlying algorithm can fail in some cases, misclassifying individual orbits under some peculiar circumstances. The performance of the algorithm benefits from a rich sampling of the traces of the SoS, which can be obtained with long numerical integration of orbits. Finally we note that the algorithm does not differentiate between the subtypes of regular orbits: resonantly trapped and untrapped orbits. Such distinction would be a useful feature, which we leave for future work. Since the result of the analysis is a probability linked to a Gaussian distribution, for the very definition of distribution, some orbits even if they have a certain nature are classified as belonging to the opposite class and create the probabilistic tails of the distribution. So while the method produces fair statistical results, it lacks in absolute classification precision.

Abstract

Within the classification of orbits in axisymmetric stellar systems, we present a new algorithm able to automatically classify the orbits according to their nature. The algorithm involves the application of the correlation integral method to the surface of section of the orbit; fitting the cumulative distribution function built with the consequents in the surface of section of the orbit, we can obtain the value of its logarithmic slope m which is directly related to the orbit’s nature: for slopes m ≈ 1 we expect the orbit to be regular, for slopes m ≈ 2 we expect it to be chaotic. With this method we have a fast and reliable way to classify orbits and, furthermore, we provide an analytical expression of the probability that an orbit is regular or chaotic given the logarithmic slope m of its correlation integral. Although this method works statistically well, the underlying algorithm can fail in some cases, misclassifying individual orbits under some peculiar circumstances. The performance of the algorithm benefits from a rich sampling of the traces of the SoS, which can be obtained with long numerical integration of orbits. Finally we note that the algorithm does not differentiate between the subtypes of regular orbits: resonantly trapped and untrapped orbits. Such distinction would be a useful feature, which we leave for future work. Since the result of the analysis is a probability linked to a Gaussian distribution, for the very definition of distribution, some orbits even if they have a certain nature are classified as belonging to the opposite class and create the probabilistic tails of the distribution. So while the method produces fair statistical results, it lacks in absolute classification precision.

Tipologia del documento

Tesi di laurea
(Laurea magistrale)

Autore della tesi

Castellani, Agnese

Relatore della tesi

Correlatore della tesi

Scuola

Corso di studio

Ordinamento Cds

DM270

Parole chiave

Correlation integral,Surface of section,Classification of orbits,Stellar orbits,Regular or chaotic orbits

Data di discussione della Tesi

28 Ottobre 2022

URI

## Altri metadati

Tipologia del documento

Tesi di laurea
(NON SPECIFICATO)

Autore della tesi

Castellani, Agnese

Relatore della tesi

Correlatore della tesi

Scuola

Corso di studio

Ordinamento Cds

DM270

Parole chiave

Correlation integral,Surface of section,Classification of orbits,Stellar orbits,Regular or chaotic orbits

Data di discussione della Tesi

28 Ottobre 2022

URI

Gestione del documento: