-
H.
Poincaré,
R.
Magini
(1899)
Les méthodes nouvelles de la mécanique céleste
Il Nuovo Cimento (1895-1900), 10
-
(2014)
Littlejohn
-
M.
Turek,
D.
Spehner,
S.
Müller,
K.
Richter
(2004)
Semiclassical form factor for spectral and matrix element fluctuations of multidimensional chaotic systems.
Physical review. E, Statistical, nonlinear, and soft matter physics, 71 1 Pt 2
-
K.
Mitchell,
J.
Delos
(2006)
A new topological technique for characterizing homoclinic tangles
Physica D: Nonlinear Phenomena, 221
-
M.
Sieber,
K.
Richter
(2001)
Correlations between periodic orbits and their rôle in spectral statistics
Physica Scripta, 2001
-
(2001)
Physica Scripta T90
-
G.
Contopoulos,
M.
Harsoula
(2015)
Convergence regions of the Moser normal forms and the structure of chaos
Journal of Physics A: Mathematical and Theoretical, 48
-
S.
Creagh,
Jonathan
Robbins,
Robert
Littlejohn
(1990)
Geometrical properties of Maslov indices in the semiclassical trace formula for the density of states.
Physical review. A, Atomic, molecular, and optical physics, 42 4
-
B.
Chirikov
(1979)
A universal instability of many-dimensional oscillator systems
Physics Reports, 52
-
E.
Bogomolny
(1992)
On dynamical zeta function.
Chaos, 2 1
-
P.
Cvitanovic,
B.
Eckhardt
(1989)
Periodic-orbit quantization of chaotic systems.
Physical review letters, 63 8
-
S.
Wiggins
(1991)
Chaotic transport in dynamical systems
-
A.
Almeida
(1989)
On the quantisation of homoclinic motion
Nonlinearity, 2
-
(2007)
Scholarpedia 2
-
F.
Haake
(1991)
Quantum signatures of chaos
-
H.
Friedrich,
Hieter
Wintgen
(1989)
The hydrogen atom in a uniform magnetic field — An example of chaos
Physics Reports, 183
-
D.
Bensimon,
L.
Kadanoff
(1984)
Extended chaos and disappearance of KAM trajectories
Physica D: Nonlinear Phenomena, 13
-
(1991)
Nonlinearity 4
-
J.
Moser
(1956)
The analytic invariants of an area‐preserving mapping near a hyperbolic fixed point
Communications on Pure and Applied Mathematics, 9
-
Jaison
Novick,
J.
Delos
(2012)
Chaotic escape from an open vase-shaped cavity. II. Topological theory.
Physical review. E, Statistical, nonlinear, and soft matter physics, 85 1 Pt 2
-
(1956)
Commun
-
K.
Mitchell,
J.
Handley,
J.
Delos,
S.
Knudson
(2003)
Geometry and topology of escape. II. Homotopic lobe dynamics.
Chaos, 13 3
-
M.
Du,
M.
Du,
J.
Delos,
J.
Delos
(1988)
Effect of closed classical orbits on quantum spectra: Ionization of atoms in a magnetic field. I. Physical picture and calculations.
Physical review. A, General physics, 38 4
-
M.
Hénon
(1976)
A two-dimensional mapping with a strange attractor
Communications in Mathematical Physics, 50
-
Kevin
Mitchell,
J.
Handley,
Brian
Tighe,
J.
Delos,
S.
Knudson
(2003)
Geometry and topology of escape. I. Epistrophes.
Chaos, 13 3
-
M.
Harsoula,
G.
Contopoulos,
C.
Efthymiopoulos
(2015)
Analytical description of the structure of chaos
Journal of Physics A: Mathematical and Theoretical, 48
-
R.
Easton
(1986)
Trellises formed by stable and unstable manifolds in the plane
Transactions of the American Mathematical Society, 294
-
R.
Easton
(1991)
Transport through chaos
Nonlinearity, 4
-
J.
Meiss
(1992)
Symplectic maps, variational principles, and transport
Reviews of Modern Physics, 64
-
M.
Du,
J.
Delos,
jbdelo
Mary
(1988)
Effect of closed classical orbits on quantum spectra: Ionization of atoms in a magnetic field. II. Derivation of formulas.
Physical review. A, General physics, 38 4
-
M.
Gutzwiller
(1971)
Periodic Orbits and Classical Quantization Conditions
Journal of Mathematical Physics, 12
-
M.
Hénon
(1969)
Numerical study of quadratic area-preserving mappings
Quarterly of Applied Mathematics, 27
-
Jaison
Novick,
M.
Keeler,
Joshua
Giefer,
J.
Delos
(2012)
Chaotic escape from an open vase-shaped cavity. I. Numerical and experimental results.
Physical review. E, Statistical, nonlinear, and soft matter physics, 85 1 Pt 2
-
G.
Ritter,
A.
Almeida,
R.
Douady
(1987)
Analytical determination of unstable periodic orbits in area preserving maps
Physica D: Nonlinear Phenomena, 29
-
I.
Esterlis,
Hal
Haggard,
Austin
Hedeman,
Robert
Littlejohn
(2014)
Maslov indices, Poisson brackets, and singular differential forms
Europhysics Letters, 106
-
Tanner,
Scherer,
Bogomolny,
Eckhardt,
Wintgen
(1991)
Quantum eigenvalues from classical periodic orbits.
Physical review letters, 67 18
-
Nathan
Argaman,
F.
Dittes,
E.
Doron,
J.
Keating,
Alexei
Kitaev,
Martin
Sieber,
U.
Smilansky
(1993)
Correlations in the actions of periodic orbits derived from quantum chaos.
Physical review letters, 71 26
-
Patrick
O'Connor,
S.
Tomsovic,
E.
Heller
(1992)
Semiclassical dynamics in the strongly chaotic regime: breaking the log time barrier
Physica D: Nonlinear Phenomena, 55
-
(1927)
Acta Math
-
H.
Lomelí,
J.
Meiss
(2008)
Resonance zones and lobe volumes for exact volume-preserving maps
Nonlinearity, 22
-
Tomsovic,
Heller
(1993)
Long-time semiclassical dynamics of chaos: The stadium billiard.
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 47 1
-
(2014)
Europhys
-
V.
Rom-Kedar
(1990)
Transport rates of a class of two-dimensional maps and flows
Physica D: Nonlinear Phenomena, 43
-
P.
So
(2007)
Unstable periodic orbits
Scholarpedia, 2
-
M.
Berry,
J.
Keating
(1990)
A rule for quantizing chaos
Journal of Physics A, 23
-
Joost
Zaat
(2005)
Chaos (2)
Huisarts en Wetenschap, 48
-
Tomsovic,
Heller
(1991)
Semiclassical dynamics of chaotic motion: Unexpected long-time accuracy.
Physical review letters, 67 6
-
R.
Balian,
C.
Bloch
(1971)
Asymptotic evaluation of the Green's function for large quantum numbers
Annals of Physics, 63
-
Jizhou
Li,
S.
Tomsovic
(2017)
Accurate determination of heteroclinic orbits in chaotic dynamical systems
Journal of Physics A: Mathematical and Theoretical, 50
-
M.
Berry,
Michael
Tabor
(1976)
Closed orbits and the regular bound spectrum
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 349
-
S.
Müller,
S.
Heusler,
P.
Braun,
F.
Haake,
A.
Altland
(2005)
Periodic-orbit theory of universality in quantum chaos.
Physical review. E, Statistical, nonlinear, and soft matter physics, 72 4 Pt 2
-
J.
Mao,
J.
Shaw,
J.
Delos
(1992)
Closed orbits and semiclassical wavefunctions in two-dimensional Hamiltonian systems
Journal of Statistical Physics, 68
-
Kevin
Mitchell,
J.
Handley,
Brian
Tighe,
Abigail
Flower,
J.
Delos
(2004)
Chaos-induced pulse trains in the ionization of hydrogen.
Physical review letters, 92 7
-
(1990)
Physica D 43
-
Sebastian
Muller,
S.
Heusler,
P.
Braun,
F.
Haake,
A.
Altland
(2004)
Semiclassical Foundation of Universality in Quantum Chaos
Physical Review Letters, 93