Since the undergraduate thesis had been written in a now obsolete text processor SIGNUM,
I do not have the entire text. While being a graduate student, a guest of Moser had
been interested in the literature of this fascinating topic and I had at that time
extracted and cleaned out the literature in ASCII form1. This has survived
and is listed below. In the summer of 2010, when we moved within Arlington, I had to get rid
of a lot of old stuff. In particular also of thousands of old papers. Being in a wet cellar for 10 years
many of my article library had started to rot. A few articles have kept dry and were
scanned in a scan orgy, where also a third of my
book library was digitized. I could rescue 15 documents
on the Stoermer problem. The evanescent paper versions are in "article heaven" now,
but their "spirit" will survive electronically here.
Of particular value is Mosers 1963 unpublished note on Stoermer problem
which I have gotten from him and which remained unpublished up to day.
A paper of Truc from 1992 (with letter of Truc) was added while I was
still a graduate student in 1992.
A Devaney article
and an article of Walt and Farley
did not make it into the literature list.
Back to my undergraduate thesis
a) Stoermerproblem
--------------------
Ar 1963 V.I. Arnold; Small divisor and stability problems in classical
and celestial mechanics, Uspekhi Mat. Nauk.18(6)(1963) pp. 85-191
2 pages [PDF]
Br 1970 Martin Braun; Particle Motions in a Magnetic Field; J.Diff.
Equ., 8 (1979), pp.294-332 [PDF]
Br 1970a Martin Braun; Structural Stability and the Stoermer Problem;
Indiana Univ. Math. J.,20 (1970),pp. 469-497 [PDF]
Br 1979 Martin Braun; The Stability of the Van Allen Radiation Belt;
SIAM J.Appl. Math. 37(3), pp.664-668 [PDF]
Br 1981 Martin Braun; Mathematical Remarks on the Van Allen
Radiation Belt; SIAM Rev.,23 (1981) ,pp. 61-94 [PDF]
Br 1981a Martin Braun; Invariant Curves,Homoclinic Points,and Ergodicity
in Area-Preserving Mappings; SIAM J. Math. Anal.,12(4)
(1981),pp.630-638
Dr 1965 Alex Dragt; Trapped orbits in a magnetic dipole field; Rev.
of Geophys.3(2) (1965), pp.255-298 [PDF]
Dr 1976 Alex Dragt, John M.Finn; Insolubility of Trapped Particle
Motion in a Magnetic Dipole Field;
J. Geophys. Res. 81,(1976) pp. 2327 [PDF]
Dr 1978 Alex Dragt, John M.Finn; Normal Form for Mirror Machine
Hamiltonians; J.Math. Phys. 20(12) (1979) pp.2649-2660 [PDF]
Ea 1980 Robert Eather; Majestic Lights ;
Fa 1983 Harald Falck-Ytter; Das Polarlicht; Verlag Freies Geistesleben,
Stuttgart 1983
He 1965 W.N.Hess,G.D.Mead and M.P.Nakada; Advances in Particle and
Field Research in the Satellite Era; Rev. of Geophys 3(4)
(1965) pp. 521-575
Mo 1963 Juergen Moser; Integrals of the Stoermer Problem; unpublished [PDF]
St 1907 Carl Stoermer; Sur les trajectoires des corpuscles electrises
dans l'espace sous l'action du magnetisme terrestre;
Arch.Sci.Phys.Nat.24, (1907)
St 1955 Carl Stoermer; The Polar Aurora; Clarendon Press, Oxford, 1955
Vo 1954 Rene de Vogelaere; Surface de section dans le proble` me
de Stoermer; Acad. Roy. Belg. Bull. Cl. Sci. 40(5)
(1954) pp. 705-714 [PDF]
Vo 1958 Rene de Vogelaere; On the structure of symmetric periodic
solutions of conservative systems with applications;
Ann. of Math. Studies,no 41, Princeton University Press,
Princeton N.J.,1958,pp. 53-84 [PDF]
b) Linked Twist maps
______________________________
Bo 1977 Rufus Bowen ; On Axiom A Diffeomorphisms ; Proc. C.B.M.S.
Regional Conf. Ser. Math.No. 35, Amer. Math. Soc.,
Providence R.I.
Be 1984 David Bensimon and Leo Kadanoff; Extended Chaos and Disappearance of
KAM Trajectories ; Physica 13D,(1984) pp.82 -89
Bu 1979 Robert Burton and Robert Easton; Ergodicity of Linked Twist
Mappings; Lecture Notes in Math.,No. 819, pp. 35-49
Br 1981a Martin Braun; Invariant Curves,Homoclinic Points,and
Ergodicity in Area-Preserving Mappings; SIAM J. Math.
Anal.,12(4) (1981),pp.630-638
De 1978 Robert L. Devaney; Subshifts of Finite Type in Linked Twist
Mappings; Proc. of the Amer. Math. Soc.,71(2)
(1978) pp. 334-338
De 1979 R.L. Devaney; Linked Twist Mappings are Almost Anosov;
Lecture Notes in Math., No. 819, pp. 121-145
De 1980 R.L. Devaney; Three Area Preserving Mappings Exhibiting
Stochastic Behavior; Lect. Notes in Pure and Appl. Math.
70, New York 1981
De 1981 R.L. Devaney; The Baker Transformation and a Mapping
Associated to the Restricted Three Body Problem; Commun.
Math. Phys. 80 (1981) pp. 465-476
Ea 1979 Robert Easton; Chain Transitivity and the Domain of Influence of
an Invariant Set; Lecture Notes in Math. No. 668
pp. 95-102
Go 1984 Daniel L.Goroff; Hyperbolic Sets for Twist Maps; Ergod.
Theory and Dyn. Sys. 5 (1985), pp.337-339
Ka 1979 Anatol Katok; Bernoulli Diffeomorphisms on Surfaces ;
Annals of Math. 110 (1979) pp. 529-547
Ma 1983 John N. Mather; Nonexistence of Invariant Circles; Ergod.
Theory and Dyn. Sys. 3(1983), pp. 301-309
Mc 1983 R.S.Mackay; Renormalisation Approach to Invariant Circles
in Area-preserving Maps; Physica 7D,(1983), pp. 283-300
Pr 1983 Feliks Przytycki; Ergodicity of Toral Linked Twist Mappings,
Ann. Scient. Ec. Norm. Sup. 4(1) (1983), pp. 345-354
Pr 1982 Feliks Przytycki; Examples of Conservative Diffeomorphisms
of the twodimensional Torus with Coexistence of Elliptic
and Stochastic Behaviour; Ergod. Theory and Dynam. Sys. 2 (1982)
pp. 439-463
Pr 1986 Feliks Przytycki; Periodic Points of Linked Twist Mappings;
Studia Mathematica, 83 (1986)
Wo 1979 Maciej Wojtkowski ; Linked Twist Mappings have the
K-Property; Nonlinear Dynamics, International Conference,
New York 1979, pp 66-76
Wo 1981 Maciej Wojtkowski; A Model Problem with Coexistence of
Stochastic and Integrable Behaviour; Comm. Math. Phys.
80(4) (1981), pp. 453-464
Wo 1982 Maciej Wojtkowski; On the Ergodic Properties of Piecewise Linear
Perturbations of the Twist Map; Ergod. Th. and Dynam. Sys.
2 (1982); pp. 525-542
c) Lyapunov exponents
___________________
Be 1984 Giancarlo Benettin; Power-Law Behaviour of Lyapunov
Exponents in some Conservative Systems; Physica D 13
(1984) pp. 211-220
Cw 1985 John B.Conway; A Course in Functional Analysis; Graduated
Texts in Math.,Springer, NewYork 1985
Co 1984 Eric Cornelis and Maciej Wojtkowski; A Criterion for the
Positivity of the Liapunov Characteristic Exponent;
Ergod. Th. and Dynam. Sys. 4 (1984) pp. 527-539
Fu 1983 H. Furstenberg and Y. Kifer; Random Matrix Products and
Measures on Projective Spaces; Israel J. Of Math. 46(1)
(1983) pp.12-36
Pe 1977 Ya.B. Pesin; Lyapunov Characteristic Exponents and Smooth
Ergodic Theorie; Russ. Math. Suveys 32(4) (1977),
pp.55-114
Sl 1980 Eric V. Slud; Products of Independent Randomly Perturbed
Matrices; in Ergodic Theorie and Dynamical Systems II,
Proceedings, Special Year, Maryland 1979-1980,Birkhaeuser
pp. 185-192
Wo 1985 Maciej Woitkowski; Invariant Families of Cones and Lyapunov
exponents; Ergod. Th. and Dynam. Sys. 5(1985) pp. 145-161
Wo 1976 Maciej Woitkowski; Principles for the Design of Billards
with Nonvanishing Lyapunov Exponents; Comm. Math. Phys.
105 (1986), pp. 391-414
Yo 1986 L.-S. Young; Random Perturbations of Matrix Cocycles;
Ergod. Th. and Dynam. Sys. 6 (1986) pp. 627-637
d) Numerical studies
_____________________________
Bi 1986 Philippe M. Binder and Roderick V. Jensen; Simulating chaotic
Behavior with Finite- State Machines; Phys. Rev. A 34(5)
(1976) pp. 4460-4463
Br 1971 A. Brahic; Numerical Study of a Simple Dynamical System;
Astron. and Astrophys. 12 (1971), pp. 98-110
Fo 1977 Joseph Ford; Relevance of Computer Experiments to the
Pure Mathematics of Integrable and Ergodic Dynamical
Systems; Soc. Math. de France, Asterisque 49 (1977)
pp. 75-92
He1964 Michel Henon and Carl Heiles; The Applicability of the Third
Integral of Motion; Astron. J. 69(1) (1964), pp. 73-80
Ra 1973 F. Rannou; Numerical Study of Discrete Plane Area-
preserving Mappings; Astron and Astrophys. 31(1974),
pp. 289-301
e) Ergodic theory
__________________
Ar 1967 V.I. Arnold and A.Avez; Proble`mes ergodiques de la me' canique
classique, Paris 1967
Ka 1975 Anatol B. Katok,Ya. G.Sinai and A.M. Stepin ; Theorie of
Dynamical Systems and General Transformation Groups
with Invariant Measure; Math. Anal. 13 (1975) pp. 129-262
Ka 1986 Anatol Katok and Jean-Marie Strelcyn; Invariant Manifolds,
Entropy and Billards : Smooth Maps with Singularities;
Lecture Notes in Mathematics No. 1222, Springer 1986
Kr 1985 Ulrich Krengel; Ergodic Theorems; New York, De Gruyter
1985
Ma 1987 Ricardo Mane' ; Ergodic Theorie and Differentiable Dynamics;
Springer EM, 3.Folge Bd.8, Berlin 1987
Si 1976 Ya.G.Sinai; Introduction to Ergodic Theorie.; Math. Notes
18, Princeton University Press 1976;
Wa 1982 Peter Walters; Introduction to Ergodic Theory; Graduated
Texts in Math. 79, Springer 1982
(1) Episodes like this (and there are many more since 1987, when this literature list was collected)
made me wary of proprietary file formats or formats which need proprietary programs to read them
and since (maybe almost obsessively) store everything of value in ASCII text form or in formats
in which open source and industry independent conversion programs are available.