Homoclinic dynamics in a restricted four-body problem: transverse connections for the saddle-focus equilibrium solution set

[1]  J. D. M. James,et al.  Spatial periodic orbits in the equilateral circular restricted four-body problem: computer-assisted proofs of existence , 2019, Celestial Mechanics and Dynamical Astronomy.

[2]  J. D. M. James,et al.  Spatial periodic orbits in the equilateral circular restricted four-body problem: computer-assisted proofs of existence , 2019, Celestial Mechanics and Dynamical Astronomy.

[3]  J. D. M. James,et al.  Chaotic motions in the restricted four body problem via Devaney's saddle-focus homoclinic tangle theorem , 2017, Journal of Differential Equations.

[4]  J. Palacián,et al.  Oscillatory motions in restricted N -body problems , 2018, Journal of Differential Equations.

[5]  Jason D. Mireles-James,et al.  Analytic Continuation of Local (Un)Stable Manifolds with Rigorous Computer Assisted Error Bounds , 2017, SIAM J. Appl. Dyn. Syst..

[6]  A. Bengochea,et al.  Horseshoe orbits in the restricted four-body problem , 2017 .

[7]  Zhikun She,et al.  Study on Chaotic Behavior of the Restricted Four-Body Problem with an Equilateral Triangle Configuration , 2017, Int. J. Bifurc. Chaos.

[8]  K. E. Papadakis.  Families of asymmetric periodic solutions in the restricted four-body problem , 2016 .

[9]  J. D. M. James,et al.  Automatic differentiation for Fourier series and the radii polynomial approach , 2016 .

[10]  Christian Reinhardt,et al.  Computing (Un)stable Manifolds with Validated Error Bounds: Non-resonant and Resonant Spectra , 2016, J. Nonlinear Sci..

[11]  K. E. Papadakis.  Families of three-dimensional periodic solutions in the circular restricted four-body problem , 2016 .

[12]  J. Burgos-García.  Families of periodic orbits in the planar Hill’s four-body problem , 2015, 1508.00875.

[13]  M. Alvarez-Ramírez,et al.  Transport orbits in an equilateral restricted four-body problem , 2015 .

[14]  M. Gidea,et al.  Hill’s approximation in a restricted four-body problem , 2014, 1412.3775.

[15]  Martha Alvarez-Ramírez,et al.  Global Regularization of a Restricted Four-Body Problem , 2014, Int. J. Bifurc. Chaos.

[16]  Jean F. Barros,et al.  Bifurcations and Enumeration of Classes of Relative Equilibria in the Planar Restricted Four-Body Problem , 2014, SIAM J. Math. Anal..

[17]  Zhikun She,et al.  The existence of a Smale horseshoe in a planar circular restricted four-body problem , 2014 .

[18]  Andrey Shilnikov,et al.  Showcase of Blue Sky Catastrophes , 2013, Int. J. Bifurc. Chaos.

[19]  Zhikun She,et al.  The existence of transversal homoclinic orbits in a planar circular restricted four-body problem , 2013 .

[20]  Joaquín Delgado,et al.  On the “blue sky catastrophe” termination in the restricted four-body problem , 2012, 1210.0144.

[21]  Joaquín Delgado,et al.  Periodic orbits in the restricted four-body problem with two equal masses , 2012, 1205.3446.

[22]  J. D. M. James,et al.  PARAMETERIZATION OF INVARIANT MANIFOLDS BY REDUCIBILITY FOR VOLUME PRESERVING AND SYMPLECTIC MAPS , 2012 .

[23]  K. E. Papadakis,et al.  Equilibrium Points and their stability in the Restricted Four-Body Problem , 2011, Int. J. Bifurc. Chaos.

[24]  K. E. Papadakis,et al.  Families of periodic orbits in the restricted four-body problem , 2011 .

[25]  Jean F. Barros,et al.  The Set of Degenerate Central Configurations in the Planar Restricted Four-Body Problem , 2011, SIAM J. Math. Anal..

[26]  Esther Barrabés,et al.  Numerical continuation of families of homoclinic connections of periodic orbits in the RTBP , 2009 .

[27]  M. Alvarez-Ramírez,et al.  Dynamical Aspects of an Equilateral Restricted Four-Body Problem , 2009 .

[28]  Eduardo S. G. Leandro.  On the central configurations of the planar restricted four-body problem , 2006 .

[29]  Ernest Fontich Julià,et al.  The parameterization method for invariant manifolds , 2006 .

[30]  Josep J. Masdemont,et al.  Homoclinic and heteroclinic transfer trajectories between planar Lyapunov orbits in the sun-earth and earth-moon systems , 2005 .

[31]  E. Doedel,et al.  Successive continuation for locating connecting orbits , 1996, Numerical Algorithms.

[32]  M. Gidea,et al.  Chaotic transfers in three- and four-body systems☆ , 2003 .

[33]  B. Schnizer,et al.  Stabilitätsuntersuchungen im restringierten Vierkörperproblem , 2003 .

[34]  R. Canosa,et al.  The parameterization method for invariant manifolds III: overview and applications , 2003 .

[35]  R. Canosa,et al.  The parameterization method for invariant manifolds II: regularity with respect to parameters , 2002 .

[36]  R. Canosa,et al.  The parameterization method for invariant manifolds I: manifolds associated to non-resonant subspaces , 2002 .

[37]  L. Lerman.  Dynamical Phenomena near a Saddle-Focus Homoclinic Connection in a Hamiltonian System , 2000 .

[38]  Shane D. Ross,et al.  Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics. , 2000, Chaos.

[39]  Björn Sandstede,et al.  A numerical toolbox for homoclinic bifurcation analysis , 1996 .

[40]  June-Gi Kim.  HOMOCLINIC ORBITS FOR HAMILTONIAN SYSTEMS , 1995 .

[41]  L. Lerman.  Complex dynamics and bifurcations in a Hamiltonian system having a transversal homoclinic orbit to a saddle focus. , 1991, Chaos.

[42]  Mark J. Friedman,et al.  Numerical computation of heteroclinic orbits , 1989 .

[43]  Carles Simó,et al.  Relative equilibrium solutions in the four body problem , 1978 .

[44]  J. Henrard,et al.  Proof of a conjecture of E. Strömgren , 1973 .

[45]  L. P. Šil'nikov,et al.  A CONTRIBUTION TO THE PROBLEM OF THE STRUCTURE OF AN EXTENDED NEIGHBORHOOD OF A ROUGH EQUILIBRIUM STATE OF SADDLE-FOCUS TYPE , 1970 .

[46]  M. Moutsoulas,et al.  Theory of orbits , 1968 .

[47]  V. Szebehely,et al.  A family of retrograde orbits around the triangular equilibrium points , 1967 .

[48]  V. Szebehely,et al.  A class of E. Stromgren's direct orbits in the restricted problem , 1967 .

[49]  Eugene Rabe,et al.  DETERMINATION AND SURVEY OF PERIODIC TROJAN ORBITS IN THE RESTRICTED PROBLEM OF THREE BODIES , 1961 .

[50]  E. Strömgren.  Connaisance actuelle des orbites dans le problème des trois corps , 1933 .

[51]  C. V. L. Charlier,et al.  Periodic Orbits , 1898, Nature.