Free Access
Issue |
Math. Model. Nat. Phenom.
Volume 8, Number 5, 2013
Bifurcations
|
|
---|---|---|
Page(s) | 155 - 172 | |
DOI | https://doi.org/10.1051/mmnp/20138510 | |
Published online | 17 September 2013 |
- G. L. Alfimov, V. M. Eleonsky, L. M. Lerman. Solitary wave solutions of nonlocal sine-Gordon equations. Chaos, v.8 (1998), No.1, 257–271. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- C. J. Amick, K. Kirschgässner. A theory of solitary water-waves in the presence of surface tension. Arch. Ration. Mech. Anal., v.105 (1989), 1–49. [CrossRef] [Google Scholar]
- C. J. Amick, J. B. McLeod. A singular perturbation problem in water waves, Stab. Appl. Anal. Contin. Media. v.1 (1992), 127–148. [Google Scholar]
- V. I. Arnold, A. G. Givental. Symplectic geometry. In the book "Encyclopaedia of Mathematical Sciences", vol. 4, Springer-Verlag, Berlin-Heidelberg-New York. [Google Scholar]
- V. I. Arnold, V. V. Kozlov, and A. I. Neishtadt. Mathematical aspects of classical and celestial mechanics. Encycl. Math. Sci., 3, Springer-Verlag, New York-Berlin, 1993. [Google Scholar]
- M. di Bernardo, C. Budd, A. Champneys, P. Kowalzcyk. Piecewise-smooth Dynamical Systems. Theory and Applications. Springer-Verlag, New York, 2008. [Google Scholar]
- M. di Bernardo, M. Feigin, S.J. Hogan, M.E. Homer. Local Analysis of C-Bifurcations in n-Dimensional Piecewise Smooth Dynamical Systems. Chaos, Solitons & Fractals, v.10 (1999), No.11, 1881–1908. [Google Scholar]
- W. Eckhaus. Singular perturbations of homoclinic orbits in R4. SIAM J. Math. Anal., v.23 (1992), 1269–1290. [CrossRef] [MathSciNet] [Google Scholar]
- M. I. Feigin. On the generation of sets of subharmonic modes in a piecewise continuous system. Prikl. Matem. Mekh., v.38 (1974), 810–818 (in Russian). [Google Scholar]
- M. I. Feigin. On the structure of C-bifurcation boundaries of piecewise continuous systems. Prikl. Matem. Mekh., v.42 (1978), 820–829 (in Russian). [Google Scholar]
- M. I. Feigin. The increasingly complex structure of the bifurcation tree of a piecewise-smooth system. Journal of Appl. Maths. Mech., v.59 (1995), 853–863. [CrossRef] [MathSciNet] [Google Scholar]
- M. I. Feigin. Forced Oscillations in Systems with Discontinuous Nonlinearities. Nauka P.H., Moscow, 1994 (in Russian). [Google Scholar]
- L. Lerman and V. Gelfreich. Slow-fast Hamiltonian Dynamics Near a Ghost Separatrix Loop. J. Math. Sci., Vol.126 (2005), No.5, 1445–1466. [MathSciNet] [Google Scholar]
- C. Grotta Ragazzo. Nonintegrability of some Hamiltonian systems, scattering and analytic continuation. Comm. Math. Phys. v.166 (1994), No. 2, 255–277. [CrossRef] [MathSciNet] [Google Scholar]
- A. Vanderbauwhede, B. Fiedler. Homoclinic period blow-up in reversible and conservative system. ZAMP, v.43 (1992), 291–318. [CrossRef] [Google Scholar]
- O. Yu. Koltsova, L. M. Lerman. Periodic and homoclinic orbits in a two-parameter unfolding of a Hamiltonian system with a homoclinic orbit to a saddle-center. Int. J. Bifurcation & Chaos. v.5 (1995), No.2, 397–408. [CrossRef] [Google Scholar]
- L. M. Lerman. Hamiltonian systems with loops of a separatrix of a saddle-center. in "Methods of the Qualitative Theory of Differential Equations", Gor’kov. Gos. Univ., Gorki, 1987, 89–103 (in Russian); Selecta Math. Soviet., v.10 (1991), 297–306 (in English). [Google Scholar]
- D. J. W. Simpson, J. D. Meiss. Simultaneous border-collision and period-doubling bifurcations. Chaos, v.19 (2009), 033146. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- A. Mielke, P. Holmes, O. O’Reilly. Cascades of homoclinic orbits to, and chaos near a Hamiltonian saddle-center. J. Dyn. Different. Equat., v.4 (1992), 95–126. [CrossRef] [Google Scholar]
- A. I. Neishtadt. On separation of motions in systems with rapidly rotating phases. Appl. Math. Mech., v.48 (1984), 197–204. [MathSciNet] [Google Scholar]
- S. Smale. Diffeomorphisms with infinitely many periodic points. in "Differential and Combinatorial Topology," Ed. S. Cairns. Princeton Math. Ser., Princeton, NJ: Princeton Univ. Press, 63–80. [Google Scholar]
- L. P. Shilnikov. On the Poincaré-Birkhoff Problem. USSR Math. Sb., v.3 (1967), 415–443. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.