TY - JOUR
T1 - Circumstellar Dust Shells of Pulsating Red Giants as Dynamical Systems
AU - Meier, S.
AU - Patzer, A. B. C.
AU - Lüttke, M.
AU - Woitke, P.
AU - Sedlmayr, E.
PY - 2000
Y1 - 2000
N2 - Miras and long-period variables (LPVs) are highly evolved, pulsating
stars on the Asymptotic Giant Branch (AGB) with massive outflows and
prominent circumstellar dust shells (CDSs). A CDS, driven by the stellar
pulsation, can be considered as a dynamical system which reveals various
kinds of complex phenomena like spatio-temporal instabilities,
bifurcations, multiperiodicity and transition to chaos. In order to
analyze the temporal behavior of the CDS standard methods known from the
theory of non-linear dynamical systems are applied. We have developed a
spherical symmetric, multi-zone description for the CDS which includes
the important physical interactions by means of non-linear coupling
terms. The corresponding Hamiltonians are derived. We present
Poincaré maps for several models with a different number of zones
in order to characterize their dynamical stability. The role of
pulsation and dust formation for the development of the dynamical
structure of the CDS is investigated. In addition, the linearized
approximation of an one-zone model is discussed with respect to the
Kolmogorov-Arnold-Moser and the Poincaré-Birkhoff theorems.
AB - Miras and long-period variables (LPVs) are highly evolved, pulsating
stars on the Asymptotic Giant Branch (AGB) with massive outflows and
prominent circumstellar dust shells (CDSs). A CDS, driven by the stellar
pulsation, can be considered as a dynamical system which reveals various
kinds of complex phenomena like spatio-temporal instabilities,
bifurcations, multiperiodicity and transition to chaos. In order to
analyze the temporal behavior of the CDS standard methods known from the
theory of non-linear dynamical systems are applied. We have developed a
spherical symmetric, multi-zone description for the CDS which includes
the important physical interactions by means of non-linear coupling
terms. The corresponding Hamiltonians are derived. We present
Poincaré maps for several models with a different number of zones
in order to characterize their dynamical stability. The role of
pulsation and dust formation for the development of the dynamical
structure of the CDS is investigated. In addition, the linearized
approximation of an one-zone model is discussed with respect to the
Kolmogorov-Arnold-Moser and the Poincaré-Birkhoff theorems.
M3 - Article
VL - 17
JO - Astronomische Gesellschaft Abstract Series
JF - Astronomische Gesellschaft Abstract Series
ER -