Access the full text.
Sign up today, get DeepDyve free for 14 days.
H. Kook, J. Meiss (1990)
Diffusion in symplectic maps.Physical review. A, Atomic, molecular, and optical physics, 41 8
M. Toda, T. Komatsuzaki, T. Konishi, R. Berry, S. Rice (2005)
Geometric structures of phase space in multidimensional chaos : applications to chemical reaction dynamics in complex systems
(2005)
M.Toda, T.Komatsuzaki, T.Konishi, R. S. Berry, S.A.Rice (Eds.)
V. I. Arnold (1964)
On the Nonstability of Dynamical Systems with Many Degrees of FreedomSoviet Math. Dokl., 5
J. Howard, R. MacKay (1987)
Linear stability of symplectic mapsJournal of Mathematical Physics, 28
R. Broucke (1969)
Stability of periodic orbits in the elliptic restricted three-body problem.AIAA Journal, 7
S. Gekle, J. Main, Th. Bartsch, T. Uzer (2006)
Phys. Rev. Lett.
A. Delshams, G. Huguet (2010)
A geometric mechanism of diffusion: Rigorous verification in a priori unstable Hamiltonian systemsJournal of Differential Equations, 250
P. Lochak (1999)
Arnold Diffusion; a Compendium of Remarks and Questions
H. Dumas, J. Laskar (1993)
Global dynamics and long-time stability in Hamiltonian systems via numerical frequency analysis.Physical review letters, 70 20
H. Dumas (2014)
The KAM Story:A Friendly Introduction to the Content, History, and Significance of Classical Kolmogorov–Arnold–Moser Theory
Franziska Onken, Steffen Lange, R. Ketzmerick, A. Bäcker (2016)
Bifurcations of families of 1D-tori in 4D symplectic maps.Chaos, 26 6
V. Arnold (2020)
Instability of Dynamical Systems with Several Degrees of FreedomHamiltonian Dynamical Systems
Y. Papaphilippou (2014)
Detecting chaos in particle accelerators through the frequency map analysis method.Chaos, 24 2
H. Broer, M. Sevryuk (2010)
KAM Theory : Quasi-periodicity in Dynamical Systems, 3
S. Gekle, J. Main, T. Bartsch, T. Uzer (2006)
Extracting multidimensional phase space topology from periodic orbits.Physical review letters, 97 10
R. I. Páez, Ch. Efthymiopoulos (2015)
Trojan Resonant DynamicsStability, and Chaotic Diffusion, for Parameters Relevant to Exoplanetary Systems, Celest. Mech. Dyn. Astr., 121
Y. Suris (1989)
Integrable mappings of the standard typeFunctional Analysis and Its Applications, 23
A. Delshams, P. Gutiérrez (1996)
Estimates on Invariant Tori near an Elliptic Equilibrium Point of a Hamiltonian SystemJournal of Differential Equations, 131
M. Firmbach, S. Lange, R. Ketzmerick, A. Bäcker (2018)
Phys. Rev. E
R. Devaney, Z. Nitecki (1979)
Shift automorphisms in the Hénon mappingCommunications in Mathematical Physics, 67
I. Georgiev, Thiago Ize, Mike Farnsworth, Ramón Montoya-Vozmediano, Alan King, Brecht Lommel, Angel Jimenez, Oscar Anson, Shinji Ogaki, Eric Johnston, A. Herubel, D. Russell, Frédéric Servant, Marcos Fajardo (2018)
ArnoldACM Transactions on Graphics (TOG), 37
R. Paez, C. Efthymiopoulos (2014)
Trojan resonant dynamics, stability, and chaotic diffusion, for parameters relevant to exoplanetary systemsCelestial Mechanics and Dynamical Astronomy, 121
N. Murray, M. Holman (2001)
The role of chaotic resonances in the Solar SystemNature, 410
A. Bäcker, J. Meiss (2018)
Elliptic Bubbles in Moser's 4D Quadratic Map: The QuadfurcationSIAM J. Appl. Dyn. Syst., 19
G. Contopoulos, M. Harsoula (2013)
3D chaotic diffusion in barred spiral galaxiesMonthly Notices of the Royal Astronomical Society, 436
R. McLachlan (1993)
Integrable four-dimensional symplectic maps of standard typePhysics Letters A, 177
M. Hénon (1976)
A two-dimensional mapping with a strange attractorCommunications in Mathematical Physics, 50
C. Froeschlé (1971)
On the number of isolating integrals in systems with three degrees of freedomAstrophysics and Space Science, 14
M. Hénon (1969)
Numerical study of quadratic area-preserving mappingsQuarterly of Applied Mathematics, 27
J. Wisdom, M. Holman (1991)
Symplectic maps for the N-body problem.The Astronomical Journal, 102
H.W. Broer, M.B. Sevryuk (2010)
KAM Theory: Quasi-Periodicity in Dynamical Systems, in Handbook of Dynamical Systems: Vol. 3, H.W. Broer, B.Hasselblatt, F.Takens (Eds.)
D. Robin, C. Steier, J. Laskar, L. Nadolski (2000)
Global dynamics of the advanced light source revealed through experimental frequency map analysis.Physical review letters, 85 3
F.M. Izrailev, B.V. Chirikov (1973)
in Proc. Colloques Internationaux du CNRS (Toulouse
L. Eliasson, B. Fayad, R. Krikorian (2013)
KAM-tori near an analytic elliptic fixed pointRegular and Chaotic Dynamics, 18
R. Gillilan, G. Ezra (1991)
Transport and turnstiles in multidimensional Hamiltonian mappings for unimolecular fragmentation: Application to van der Waals predissociationJournal of Chemical Physics, 94
P. Lochak (1999)
Arnold Diffusion: A Compendium of Remarks and Questions, in Hamiltonian Systems with Three or More Degrees of Freedom (S’Agaró, 1995)
R. Warnock, R. Ruth (1992)
Long-term bounds on nonlinear Hamiltonian motionPhysica D: Nonlinear Phenomena, 56
P. Cincotta (2002)
Arnold diffusion: an overview through dynamical astronomyNew Astronomy Reviews, 46
J.E. Howard, A. J. Lichtenberg (1986)
Lieberman,M.A., and CohenR.H., Four-DimensionalMapping Model for Two-Frequency Electron Cyclotron Resonance Heating, Physica D, 20
R. Broucke (1969)
Stability of Periodic Orbits in the EllipticRestricted Three-Body Problem, AIAA J., 7
J. Daquin, A. Rosengren, E. Alessi, F. Deleflie, G. Valsecchi, A. Rossi (2015)
The dynamical structure of the MEO region: long-term stability, chaos, and transportCelestial Mechanics and Dynamical Astronomy, 124
J. Howard, A. Lichtenberg, M. Lieberman, R. Cohen (1986)
Four-dimensional mapping model for two-frequency electron cyclotron resonance heatingPhysica D: Nonlinear Phenomena, 20
J. Moser (1962)
On invariant curves of area-preserving mappings of an anulus
Martin Richter, Steffen Lange, A. Bäcker, R. Ketzmerick (2013)
Visualization and comparison of classical structures and quantum states of four-dimensional maps.Physical review. E, Statistical, nonlinear, and soft matter physics, 89 2
Paranjothy Manikandan, S. Keshavamurthy (2014)
Dynamical traps lead to the slowing down of intramolecular vibrational energy flowProceedings of the National Academy of Sciences, 111
(1973)
Some Numerical Experiments with a Nonlinear Mapping: Stochastic Component
F. Onken, S. Lange, R. Ketzmerick, A. Bäcker (2016)
Chaos
Markus Firmbach, Steffen Lange, R. Ketzmerick, A. Bäcker (2018)
Three-dimensional billiards: Visualization of regular structures and trapping of chaotic trajectories.Physical review. E, 98 2-1
H. Waalkens, R. Schubert, Stephen Wiggins (2007)
Wigner's dynamical transition state theory in phase space: classical and quantumNonlinearity, 21
P. Ramachandran, G. Varoquaux (2010)
Mayavi: 3D Visualization of Scientific DataComputing in Science & Engineering, 13
T. Bountis, H. Segur, F. Vivaldi (1982)
Integrable Hamiltonian Systems and the Painleve PropertyPhysical Review A, 25
O. Castro-Orgaz, W. Hager (2019)
and sShallow Water Hydraulics
C. Simó (1999)
Hamiltonian systems with three or more degrees of freedom
Steffen Lange, Martin Richter, Franziska Onken, A. Backer, Roland Physik, Center Dynamics, Technischer Systeme (2013)
Global structure of regular tori in a generic 4D symplectic map.Chaos, 24 2
J. Moser (1994)
On quadratic symplectic mappingsMathematische Zeitschrift, 216
H. Waalkens, R. Schubert, S. Wiggins (2008)
Nonlinearity
P. Gaspard, S. Rice (1989)
Hamiltonian mapping models of molecular fragmentationThe Journal of Physical Chemistry, 93
J. Daquin, A. J. Rosengren, E.M. Alessi, F. Deleflie, G.B. Valsecchi, A. Rossi (2016)
The Dynamical Structure of the MEO Region: Long-Term StabilityChaos, and Transport, Celest. Mech. Dyn. Astr., 124
In 1994, Jürgen Moser generalized Hénon’s area-preserving quadratic map to obtain a normal form for the family of four-dimensional, quadratic, symplectic maps. This map has at most four isolated fixed points. We show that the bounded dynamics of Moser’s six parameter family is organized by a codimension-three bifurcation, which we call a quadfurcation, that can create all four fixed points from none.
Regular and Chaotic Dynamics – Springer Journals
Published: Dec 12, 2018
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.