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Positive topological entropy for multidimensional perturbations of topologically crossing homoclinicity
1. | Department of Applied Mathematics, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 300, Taiwan, Taiwan |
References:
[1] |
K. Burns and H. Weiss, A geometric criterion for positive topological entropy, Comm. Math. Phys., 172 (1995), 95-118.
doi: 10.1007/BF02104512. |
[2] |
M. Gidea and C. Robinson, Topologically crossing heteroclinic connections to invariant tori, J. Differential Equations, 193 (2003), 49-74.
doi: 10.1016/S0022-0396(03)00065-2. |
[3] |
M. Gidea and P. Zgliczyński, Covering relations for multidimensional dynamical systems-II, J. Differential Equations, 202 (2004), 59-80.
doi: 10.1016/j.jde.2004.03.014. |
[4] |
J. Juang, M.-C. Li and M. Malkin, Chaotic difference equations in two variables and their multidimensional perturbations, Nonlinearity, 21 (2008), 1019-1040.
doi: 10.1088/0951-7715/21/5/007. |
[5] |
M.-C. Li and M.-J. Lyu, Topological dynamics for multidimensional perturbations of maps with covering relations and Liapunov condition, J. Differential Equations, 250 (2011), 799-812.
doi: 10.1016/j.jde.2010.06.019. |
[6] |
M.-C Li, M.-J. Lyu and P. Zgliczyński, Topological entropy for multidimensional perturbations of snap-back repellers and one-dimensional maps, Nonlinearity, 21 (2008), 2555-2567.
doi: 10.1088/0951-7715/21/11/005. |
[7] |
M.-C. Li and M. Malkin, Topological horseshoes for perturbations of singular difference equations, Nonlinearity, 19 (2006), 795-811.
doi: 10.1088/0951-7715/19/4/002. |
[8] |
M. Misiurewicz and P. Zgliczyński, Topological entropy for multidimensional perturbations of one-dimensional maps, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 11 (2001), 1443-1446.
doi: 10.1142/S021812740100281X. |
[9] |
C. Robinson, "Dynamical Systems: Stability, Symbolic Dynamics, and Chaos," 2nd edition, CRC Press, Boca Raton, FL, 1999. |
[10] |
J. T. Schwartz, "Nonlinear Functional Analysis," Gordon and Breach Science Publishers, New York, 1969. |
[11] |
L.-S. Young, Chaotic phenomena in three settings: Large, noisy and out of equilibrium, Nonlinearity, 21 (2008), T245-T252.
doi: 10.1088/0951-7715/21/11/T04. |
[12] |
P. Zgliczyński, Fixed point index for iterations, topological horseshoe and chaos, Topological Methods in Nonlinear Analysis, 8 (1996), 169-177. |
[13] |
P. Zgliczyński, Computer assisted proof of chaos in the Rössler equations and in the Hénon map, Nonlinearity, 10 (1997), 243-252.
doi: 10.1088/0951-7715/10/1/016. |
[14] |
P. Zgliczyński and M. Gidea, Covering relations for multidimensional dynamical systems, J. Differential Equations, 202 (2004), 32-58.
doi: 10.1016/j.jde.2004.03.013. |
show all references
References:
[1] |
K. Burns and H. Weiss, A geometric criterion for positive topological entropy, Comm. Math. Phys., 172 (1995), 95-118.
doi: 10.1007/BF02104512. |
[2] |
M. Gidea and C. Robinson, Topologically crossing heteroclinic connections to invariant tori, J. Differential Equations, 193 (2003), 49-74.
doi: 10.1016/S0022-0396(03)00065-2. |
[3] |
M. Gidea and P. Zgliczyński, Covering relations for multidimensional dynamical systems-II, J. Differential Equations, 202 (2004), 59-80.
doi: 10.1016/j.jde.2004.03.014. |
[4] |
J. Juang, M.-C. Li and M. Malkin, Chaotic difference equations in two variables and their multidimensional perturbations, Nonlinearity, 21 (2008), 1019-1040.
doi: 10.1088/0951-7715/21/5/007. |
[5] |
M.-C. Li and M.-J. Lyu, Topological dynamics for multidimensional perturbations of maps with covering relations and Liapunov condition, J. Differential Equations, 250 (2011), 799-812.
doi: 10.1016/j.jde.2010.06.019. |
[6] |
M.-C Li, M.-J. Lyu and P. Zgliczyński, Topological entropy for multidimensional perturbations of snap-back repellers and one-dimensional maps, Nonlinearity, 21 (2008), 2555-2567.
doi: 10.1088/0951-7715/21/11/005. |
[7] |
M.-C. Li and M. Malkin, Topological horseshoes for perturbations of singular difference equations, Nonlinearity, 19 (2006), 795-811.
doi: 10.1088/0951-7715/19/4/002. |
[8] |
M. Misiurewicz and P. Zgliczyński, Topological entropy for multidimensional perturbations of one-dimensional maps, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 11 (2001), 1443-1446.
doi: 10.1142/S021812740100281X. |
[9] |
C. Robinson, "Dynamical Systems: Stability, Symbolic Dynamics, and Chaos," 2nd edition, CRC Press, Boca Raton, FL, 1999. |
[10] |
J. T. Schwartz, "Nonlinear Functional Analysis," Gordon and Breach Science Publishers, New York, 1969. |
[11] |
L.-S. Young, Chaotic phenomena in three settings: Large, noisy and out of equilibrium, Nonlinearity, 21 (2008), T245-T252.
doi: 10.1088/0951-7715/21/11/T04. |
[12] |
P. Zgliczyński, Fixed point index for iterations, topological horseshoe and chaos, Topological Methods in Nonlinear Analysis, 8 (1996), 169-177. |
[13] |
P. Zgliczyński, Computer assisted proof of chaos in the Rössler equations and in the Hénon map, Nonlinearity, 10 (1997), 243-252.
doi: 10.1088/0951-7715/10/1/016. |
[14] |
P. Zgliczyński and M. Gidea, Covering relations for multidimensional dynamical systems, J. Differential Equations, 202 (2004), 32-58.
doi: 10.1016/j.jde.2004.03.013. |
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