Table Of ContentAstrophysics and Space Science Proceedings
Chaos in Astronomy
Conference 2007
G. Contopoulos
Editor
ResearchCenterforAstronomy,AcademyofAthens,
Athens,Greece
P.A. Patsis
Editor
ResearchCenterforAstronomy,AcademyofAthens,
Athens,Greece
ABC
Editors
G.Contopoulos
P.A.Patsis
ResearchCenterforAstronomy
AcademyofAthens
SoranouEfessiou4
11527Athens
Greece
ISBN:978-3-540-75825-9 e-ISBN:978-3-540-75826-6
DOI:10.1007/978-3-540-75826-6
LibraryofCongressControlNumber:2008930098
(cid:176)c 2009 Springer-VerlagBerlinHeidelberg
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In memory of Prof. Nikos Voglis
Preface
The conference Chaos in Astronomy was held in Athens from 17 to 20
September 2007 and was dedicated to the memory of Nikos Voglis, who was
directoroftheResearchCenterforAstronomyoftheAcademyofAthensuntil
his death on 9 February 2007. It was attended by 73 registered participants
coming from 18 different countries. A total of 40 oral papers were delivered
includingaconferencesummary.Furthermore16posterswerepresented.The
conference was the main event in a series of talks, public lectures and dis-
cussion meetings about “Chaos in Astronomy” that have taken place at the
Research Center for Astronomy. We underline three special talks that have
beengivenbyD.Kazanas(NASA-GoddardSpaceFlightCenter),D.Lynden-
Bell (Cambridge, UK) and C. Tsallis (Brazilian Academy of Science).
Themainsponsoroftheconferencewasthe“AlexanderS.Onassis”Foun-
dation. In addition the conference has been supported by the General Sec-
retariat for Research and Technology, the National Observatory of Athens,
and the Hellenic Ministry of Culture. We are grateful to all sponsors for their
generosity.
We also express our gratitude to the Academy of Athens and to the di-
rectorshipoftheBiomedical ResearchFoundation, wheretheconferencetook
place.
The objective of the conference was to bring together experts from all
branches of Astronomy that work on nonlinear phenomena and Chaos. The
scientific discussions concentrated in applications of the Chaos Theory to
Galactic Dynamics. We discussed the chaotic motion of stars in the spiral
arms of barred spiral galaxies, the chaotic phenomena associated with the
boxy/peanutmorphologyofthecentralpartsofgalacticdisks,thechaoticmo-
tionofstarsinthesolarneighborhood,theclassificationoforderedandchaotic
orbits in elliptical galaxies, and in general the role of nonlinear phenomena
in the observed structure of galaxies. Besides Galactic Dynamics, there were
manytalksaboutnonlinear phenomenaandchaosinCelestialMechanics,ac-
cretiondisksaroundBlackHoles,inSolarPhysicsandCosmology.Thepresent
VII
VIII Preface
volume offers the state of the art of the ongoing discussions in topics of the
Chaos theory in all these fields.
The present proceeding contains 49 papers. All submitted papers were
refereed and almost all were revised. The procedure followed was the same as
whenpapersaresubmittedtoaresearchjournal.Wethankalltheparticipants
for their contributions and the referees for their help.
Athens G. Contopoulos
August 2008 P.A. Patsis
Contents
List of Contributors ...........................................XV
Nikolaos Voglis (1948–2007)
G. Contopoulos ..................................................XXI
Part I Galactic Dynamics
Ordered and Chaotic Orbits in Spiral Galaxies
G. Contopoulos .................................................. 3
Order and Chaos in Spiral Galaxies
Seen through their Morphology
P. Grosbøl ...................................................... 23
The Flow through the Arms of Normal and Barred-Spiral
Galaxies
P.A. Patsis ..................................................... 33
Ansae in Barred Galaxies, Observations and Simulations
I. Martinez-Valpuesta ............................................ 45
Orbital Structure in Barred Galaxies and the Role
of Chaos
M. Harsoula, G. Contopoulos, and C. Kalapotharakos................. 53
Chaos in Galaxies
D. Pfenniger .................................................... 63
Boxy/Peanut Bulges: Formation, Evolution and Properties
E. Athanassoula and I. Martinez-Valpuesta.......................... 77
IX
X Contents
Invariant Manifolds as Building Blocks for the Formation
of Spiral Arms and Rings in Barred Galaxies
M. Romero-Go´mez, E. Athanassoula, J.J. Masdemont
and C. Garc´ıa-Go´mez ............................................ 85
Secular Instabilities of Stellar Systems: Slow Mode Approach
E.V. Polyachenko, V.L. Polyachenko, and I.G. Shukhman............. 93
Stellar Velocity Distribution in Galactic Disks
Ch. Theis and E. Vorobyov........................................105
Dynamical Study of 2D and 3D Barred Galaxy Models
T. Manos and E. Athanassoula ....................................115
Chaos in the Mergers of Galaxies
P.O. Vandervoort ................................................123
Hamiltonian Normal Forms and Galactic Potentials
G. Pucacco......................................................137
Local Phase Space: Shaped by Chaos?
D. Chakrabarty ..................................................151
Barred Galaxies: An Observer’s Perspective
Dimitri A. Gadotti ...............................................159
Invariant Manifolds and the Spiral Arms of Barred Galaxies
C. Efthymiopoulos, P. Tsoutsis, C. Kalapotharakos
and G. Contopoulos ..............................................173
Collisional N-Body Simulations and Time-Dependent Orbital
Complexity
N.T. Faber ......................................................183
Resonances in Galactic and Circumstellar Disks
A.C. Quillen ....................................................191
Regular and Chaotic Motion in Elliptical Galaxies
J.C. Muzzio .....................................................203
Orbital Distributions and Self-Consistency
in Elliptical Galaxies
C. Kalapotharakos ...............................................215
The Connection Between Orbits and Isophotal Shape
in Elliptical Galaxies
R. Jesseit, T. Naab, and A. Burkert................................225
Contents XI
Gas Orbits in a Spiral Potential
G.C. Go´mez and M.A. Martos.....................................231
The Structure of the Phase Space in Galactic Potentials
of Three Degrees of Freedom
M. Katsanikas, P.A. Patsis, and L. Zachilas ........................235
Regular and Chaotic Orbits in Narrow 2D Bar Models
D.E. Kaufmann and P.A. Patsis...................................241
The Coalescence of Invariant Manifolds in Barred-Spiral
Galaxies
P. Tsoutsis and C. Efthymiopoulos .................................247
Part II Celestial Mechanics
Chaotic Dynamics in Planetary Systems
R. Dvorak.......................................................255
Routes to Chaos in Resonant Extrasolar Planetary Systems
J.D. Hadjidemetriou and G. Voyatzis...............................269
Prometheus and Pandora, the Champions of Dynamical
Chaos
I.I. Shevchenko ..................................................285
Planets in Multiple Star Systems: A Symplectic Approach
P.E. Verrier and N.W. Evans .....................................293
Stabilized Chaos in the Sitnikov Problem
A.R. Dzhanoev, A. Loskutov, J.E. Howard, and M.A.F. S´anju .........301
Part III Fundamental Concepts and Methods
Nonextensive Statistical Mechanics – An Approach
to Complexity
C. Tsallis .......................................................309
Absolute Versus Relative Motion in Mechanics
D. Lynden-Bell ..................................................319
Far Fields, from Electrodynamics to Gravitation,
and the Dark Matter Problem
A. Carati, S.L. Cacciatori, and L. Galgani ..........................325
XII Contents
Distribution Functions for Galaxies using Quadratic
Programming
V. Dury, S. De Rijcke, V. Debattista, and H. Dejonghe ...............337
Chaos Analysis Using the Patterns Method
I. Sideris .......................................................347
On the Topology of Regions of 3-D Particle Motions
in Annular Configurations of n Bodies with a Central
Post-Newtonian Potential
T. Kalvouridis...................................................357
The Average Power-Law Growth of Deviation Vector
and Tsallis Entropy
G. Lukes-Gerakopoulos, N. Voglis, and C. Efthymiopoulos.............363
Global Dynamics of Coupled Standard Maps
T. Manos, Ch. Skokos, and T. Bountis .............................367
Part IV Other Astronomical Systems
The Chaotic Light Curves of Accreting Black Holes
D. Kazanas .....................................................375
3D Accretion Discs Dynamics: Numerical Simulations
D.V. Bisikalo....................................................387
Growth of Density Fluctuations at the Time
of Leptogenesis
E.A. Paschos....................................................399
Fully Developed Turbulence in Accretion Discs of Binary
Stars: Turbulent Viscosity Coefficient and Power Spectrum
A.M. Fridman, D.V. Bisikalo, A.A. Boyarchuk, L. Pustil’nik,
and Y.M. Torgashin .............................................403
Solar and Stellar Active Regions
Loukas Vlahos ...................................................423
Chaos and Self-Organization in Solar Flares: A Critical
Analysis of the Present Approach
L. Pustil’nik.....................................................435
Charged Particles’ Acceleration through Reconnecting
Current Sheets in Solar Flares
C. Gontikakis, C. Efthymiopoulos, and A. Anastasiadis ...............449
