[1] Milnor, J. and Thurston, W. On iterated maps of the interval. Dynamical Systems, Lecture Notes in Mathematics (ed. Alexander, J. C.), Springer, New York, 465–563 (1988)
[2] Barrio, R., Shilnikov, A., and Shilnikov, L. Kneadings, symbolic dynamics and painting Lorenz chaos. International Journal of Bifurcation and Chaos, 22, 1230016 (2012)
[3] Caneco, A., Grácio, C., and Rocha, J. Kneading theory analysis of the Duffing equation. Chaos Solitons Fractals, 42, 1529–1538 (2009)
[4] Guckenheimer, J. and Scheper, C. A geometric model for mixed-mode oscillations in a chemical system. SIAM Journal on Applied Dynamical Systems, 10, 92–128 (2011)
[5] Cvitanovi?, P. Periodic orbits as the skeleton of classical and quantum chaos. Physica D, 51, 138–151 (1991)
[6] Cvitanovi?, P., Gunaratne, G., and Procaccia, I. Topological and metric properties of Hénon-type strange attractors. Physical Review A, 38, 1503–1520 (1988)
[7] Hénon, M. A two-dimensional mapping with a strange attractor. Communications in Mathematical Physics, 50, 69–77 (1976)
[8] Lozi, R. Un attracteur étrange du type attracteur de Hénon. Journal de Physique, 39, 9–10 (1978)
[9] Mendoza, V. Proof of the pruning front conjecture for certain Hénon parameters. Nonlinearity, 26, 679–690 (2013)
[10] Mendoza, V. A note about pruning and Hénon Maps. Qualitative Theory of Dynamical Systems, 12, 443–448 (2013)
[11] Hagiwara, R. and Shudo, A. An algorithm to prune the area-preserving Hénon map. Journal of Physics A: Mathematical and General, 37, 10521–10543 (2004)
[12] Hagiwara, R. and Shudo, A. Grammatical complexity for two-dimensional maps. Journal of Physics A: Mathematical and General, 37, 10545–10559 (2004)
[13] Jaeger, L. and Kantz, H. Structure of generating partitions for two-dimensional maps. Journal of Physics A: Mathematical and General, 30, 567–576 (1997)
[14] Ishii, Y. Towards a kneading theory for Lozi mappings I: a solution of the pruning front conjecture and the first tangency problem. Nonlinearity, 10, 731–747 (1997)
[15] Ishii, Y. Towards a kneading theory for Lozi mappings II: monotonicity of the topological entropy and Hausdorff dimension of attractors. Communications in Mathematical Physics, 190, 375–394 (1997)
[16] Whiston, G. S. Global dynamics of a vibro-impacting linear oscillator. Journal of Sound and Vibration, 118, 395–429 (1987)
[17] Whiston, G. S. Singularities in vibro-impact dynamics. Journal of Sound and Vibration, 152, 427–460 (1992)
[18] Nordmark, A. B. Non-periodic motion caused by grazing incidence in an impact oscillator. Journal of Sound and Vibration, 145, 279–297 (1991)
[19] Molenaar, J., de Weger, J., and van de Water, W. Mappings of grazing impact oscillators. Nonlinearity, 14, 301–321 (2001)
[20] Di Bernardo, M., Budd, C. J., Champneys, A. R., and Kowalczyk, P. Piecewise-Smooth Dynamical Systems: Theory and Applications, Springer-Verlag, London (2008)
[21] Yue, Y. and Xie, J. H. Symmetry, cusp bifurcation and chaos of an impact oscillator between two rigid sides. Applied Mathematics and Mechanics (English Edition), 28, 1109–1127 (2007) DOI 10.1007/s10483-007-0813-z
[22] Leine, R. I. and Nijmeijer, H. Dynamics and Bifurcations of Non-Smooth Mechanical Systems. Springer-Verlag, Berlin (2004)
[23] Di Bernardo, M., Kowalczyk, P., and Nordmark, A. B. Sliding bifurcations: a novel mechanism for the sudden onset of chaos in dry-friction oscillators. International Journal of Bifurcation and Chaos, 13, 2935–2948 (2003)
[24] Kowalczyka, P. and Piiroinenb, P. T. Two-parameter sliding bifurcations of periodic solutions in a dry-friction oscillator. Physica D, 237, 1053–1073 (2008)
[25] Guardia, T. M., Seara, T., and Hogan, S. J. An analytical approach to codimension-2 sliding bifurcations in the dry friction oscillator. SIAM Journal on Applied Dynamical Systems, 9, 769– 798 (2010)
[26] Guo, Y. and Xie, J. H. Neimark-Sacker (N-S) bifurcation of oscillator with dry friction in 1:4 strong resonance. Applied Mathematics and Mechanics (English Edition), 34, 27–36 (2013) DOI 10.1007/s10483-013-1650-9
[27] Belykh, V. Qualitative Methods of the Theory of Nonlinear Oscilaltions in Point Systems, Gorki University Press, Gorki (1980)
[28] Tél, T. Fractal dimension of the strange attractor in a piecewise linear two-dimensional map. Physics Letters A, 97, 219–223 (1983)
[29] Young, L. S. Bowen-Ruelle measures for certain piecewise hyperbolic maps. Transactions of the American Mathematical Society, 287, 41–48 (1985)
[30] Pesin, Y. B. Dynamical systems with generalized hyperbolic attractors: hyperbolic, ergodic and topological properties. Ergodic Theory and Dynamical Systems, 12, 123–151 (1992)
[31] Afraimovich, V., Chernov, N., and Sataev, E. Statistical properties of 2-D generalized hyperbolic attractors. Chaos, 5, 238–252 (1995)
[32] Young, L. S. Statistical properties of dynamical systems with some hyperbolicity. Annals of Mathematics, 147, 585–650 (1998) |