Abstract
The purpose of this paper is to analyze the chaotic behavior that can arise on a type-IX cosmological model using methods from dynamic systems theory and symbolic dynamics. Specifically, instead of the Belinski-Khalatnikov-Lifschitz model, we use the iterates of a monotonously increasing map of the circle with a discontinuity, and for the Hamiltonian dynamics of Misner's Mixmaster model we introduce the iterates of a noninvertible map. An equivalence between these two models can easily be brought upon by translating them in symbolic dynamical terms. The resulting symbolic orbits can be inserted in an ordered tree structure set, and so we can present an effective counting and referentation of all period orbits.
Citation Formats
Bugalho, H, da Silva, A R, and Ramos, J S.
The order of chaos on a Bianch IX cosmological model.
United Kingdom: N. p.,
1986.
Web.
doi:10.1007/BF00763451.
Bugalho, H, da Silva, A R, & Ramos, J S.
The order of chaos on a Bianch IX cosmological model.
United Kingdom.
https://doi.org/10.1007/BF00763451
Bugalho, H, da Silva, A R, and Ramos, J S.
1986.
"The order of chaos on a Bianch IX cosmological model."
United Kingdom.
https://doi.org/10.1007/BF00763451.
@misc{etde_6752365,
title = {The order of chaos on a Bianch IX cosmological model}
author = {Bugalho, H, da Silva, A R, and Ramos, J S}
abstractNote = {The purpose of this paper is to analyze the chaotic behavior that can arise on a type-IX cosmological model using methods from dynamic systems theory and symbolic dynamics. Specifically, instead of the Belinski-Khalatnikov-Lifschitz model, we use the iterates of a monotonously increasing map of the circle with a discontinuity, and for the Hamiltonian dynamics of Misner's Mixmaster model we introduce the iterates of a noninvertible map. An equivalence between these two models can easily be brought upon by translating them in symbolic dynamical terms. The resulting symbolic orbits can be inserted in an ordered tree structure set, and so we can present an effective counting and referentation of all period orbits.}
doi = {10.1007/BF00763451}
journal = []
volume = {18:12}
journal type = {AC}
place = {United Kingdom}
year = {1986}
month = {Dec}
}
title = {The order of chaos on a Bianch IX cosmological model}
author = {Bugalho, H, da Silva, A R, and Ramos, J S}
abstractNote = {The purpose of this paper is to analyze the chaotic behavior that can arise on a type-IX cosmological model using methods from dynamic systems theory and symbolic dynamics. Specifically, instead of the Belinski-Khalatnikov-Lifschitz model, we use the iterates of a monotonously increasing map of the circle with a discontinuity, and for the Hamiltonian dynamics of Misner's Mixmaster model we introduce the iterates of a noninvertible map. An equivalence between these two models can easily be brought upon by translating them in symbolic dynamical terms. The resulting symbolic orbits can be inserted in an ordered tree structure set, and so we can present an effective counting and referentation of all period orbits.}
doi = {10.1007/BF00763451}
journal = []
volume = {18:12}
journal type = {AC}
place = {United Kingdom}
year = {1986}
month = {Dec}
}