References
- K. Bolejko, Structure formation in the quasispherical Szekeres model, Phys. Rev. D 73 (2006) 123508. doi: 10.1103/PhysRevD.73.123508
- K. Bolejko, A. Krasiński, C. Hellaby, M.–N. Célérier, Structures in the Universe by exact methods — formation, evolution, interactions, (Cambridge University Press, 2010).
- M. Bruni, S. Matarrese and O. Pantano, Dynamics of Silent Universes, Astroph. J. 445 (1995) 958–977. doi: 10.1086/175755
- G. Darboux, Mémoire sur les équations différentielles algébriques du premier ordre et du premier degré (Mélanges), Bull. Sc. Math. 2ème série, 2 (1878) 60–96. 123–144, 151–200.
- A. Goriely, Integrability and Nonintegrability of Dynamical Systems, Adv. Series in Nonl. Dyn. 19 (World Scientific, Singapore, 2001).
- J. Llibre and C. Valls, Darboux integrability of a generalized Friedmann-Robertson-Walker Hamiltonian system, J. Nonlinear Math. Phys. Vol. 20 No. 3 (2013) 394–406. doi: 10.1080/14029251.2013.854482
- S. Lynch, Dynamical Systems with Applications using Mathematica®, (Birkhäuser, Boston, 2007).
- Wolfram Research, Inc., Mathematica, ver. 10.0 (Champaign, IL 2015).
- L. Perko, Differential Equations and Dynamical Systems, Texts in Applied Mathematics 7 (Springer-Verlag, New York, 2008).
- R. A. Sussman and K. Bolejko, A novel approach to the dynamics of Szekeres dust models, Classical and Quantum Gravity 29 (2012) 065018. doi: 10.1088/0264-9381/29/6/065018
- P. Szekeres, A Class of Inhomogeneous Cosmological Models, Commun. Math. Phys. 41 (1975) 55–64. doi: 10.1007/BF01608547
- H. Yoshida, Necessary conditions for the existence of algebraic first integrals I: Kowalevski’s Exponents, Celest. Mech. 31 (1983) 363–379. doi: 10.1007/BF01230292
- H. Yoshida, Necessary conditions for the existence of algebraic first integrals II: Condition for Algebraic Integrability, Celest. Mech. 31 (1983) 381–399. doi: 10.1007/BF01230293