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Box dimension and bifurcations of onedimensional discrete dynamical systems
1.  Department of Applied Mathematics, Faculty of Electrical Engineering and Computing, Unska 3, 10000 Zagreb, Croatia 
References:
[1] 
D. K. Arrowsmith and C. M. Place, "An Introduction to Dynamical Systems,", Cambridge University Press, (1990). Google Scholar 
[2] 
F. Balibrea and J. C. Valverde, Bifurcations under nondegenerated conditions of higher degree and a new simple proof of the HopfNeimarkSacker bifurcation theorem,, J. Math. Anal. Appl., 237 (1999), 93. doi: 10.1006/jmaa.1999.6460. Google Scholar 
[3] 
F. Balibrea and J. C. Valverde, Cusp and generalized flip bifurcations under higher degree conditions,, Nonlinear Anal., 52 (2003), 405. doi: 10.1016/S0362546X(01)009087. Google Scholar 
[4] 
N. Elezović, V. Županović and D. Žubrinić, Box dimension of trajectories of some discrete dynamical systems,, Chaos Solitons Fractals, 34 (2007), 244. doi: 10.1016/j.chaos.2006.03.060. Google Scholar 
[5] 
K. Falconer, "Fractal Geometry: Mathematical Foundations and Applications,", John Wiley & Sons, (1990). Google Scholar 
[6] 
Y. A. Kuznetsov, "Elements of Applied Bifurcation Theory,", 2^{nd} edition, 112 (1998). Google Scholar 
[7] 
M. L. Lapidus and C. Pomerance, The Riemann zetafunction and the onedimensional WeylBerry conjecture for fractal drums,, Proc. London Math. Soc. (3), 66 (1993), 41. Google Scholar 
[8] 
P. Mattila, "Geometry of Sets and Measures in Euclidean Spaces. Fractals and Rectifiability,", Cambridge Studies in Advanced Mathematics, 44 (1995). Google Scholar 
[9] 
J. Palis and F. Takens, "Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations. Fractal Dimensions and Infinitely Many Attractors,", Cambridge Studies in Advanced Mathematics, 35 (1993). Google Scholar 
[10] 
M. Pašić, MinkowskiBouligand dimension of solutions of the onedimensional $p$Laplacian,, J. Differential Equations, 190 (2003), 268. doi: 10.1016/S00220396(02)001493. Google Scholar 
[11] 
M. Pašić, D. Žubrinić and V. Županović, Oscillatory and phase dimensions of solutions of some secondorder differential equations,, Bull. Sci. Math., 133 (2009), 859. Google Scholar 
[12] 
L. Perko, "Differential Equations and Dynamical Systems,", 2^{nd} edition, 7 (1996). Google Scholar 
[13] 
C. Tricot, "Curves and Fractal Dimension,", With a foreword by Michel Mendès France, (1995). Google Scholar 
[14] 
S. Wiggins, "Introduction to Applied Nonlinear Dynamical Systems and Chaos,", 2^{nd} edition, 2 (2003). Google Scholar 
[15] 
D. Žubrinić, Analysis of Minkowski content of fractal sets and applications,, Real Anal. Exchange, 31 (): 315. Google Scholar 
[16] 
D. Žubrinić and V. Županović, Fractal dimension in dynamics,, in, (2006), 394. Google Scholar 
[17] 
D. Žubrinić and V. Županović, Poincaré map in fractal analysis of spiral trajectories of planar vector fields,, Bull. Belg. Math. Soc. Simon Stevin, 15 (2008), 947. Google Scholar 
[18] 
D. Žubrinić and V. Županović, Fractal analysis of spiral trajectories of some planar vector fields,, Bull. Sci. Math., 129 (2005), 457. Google Scholar 
[19] 
D. Žubrinić and V. Županović, Fractal analysis of spiral trajectories of some vector fields in $\mathbbR^3$,, C. R. Math. Acad. Sci. Paris, 342 (2006), 959. Google Scholar 
show all references
References:
[1] 
D. K. Arrowsmith and C. M. Place, "An Introduction to Dynamical Systems,", Cambridge University Press, (1990). Google Scholar 
[2] 
F. Balibrea and J. C. Valverde, Bifurcations under nondegenerated conditions of higher degree and a new simple proof of the HopfNeimarkSacker bifurcation theorem,, J. Math. Anal. Appl., 237 (1999), 93. doi: 10.1006/jmaa.1999.6460. Google Scholar 
[3] 
F. Balibrea and J. C. Valverde, Cusp and generalized flip bifurcations under higher degree conditions,, Nonlinear Anal., 52 (2003), 405. doi: 10.1016/S0362546X(01)009087. Google Scholar 
[4] 
N. Elezović, V. Županović and D. Žubrinić, Box dimension of trajectories of some discrete dynamical systems,, Chaos Solitons Fractals, 34 (2007), 244. doi: 10.1016/j.chaos.2006.03.060. Google Scholar 
[5] 
K. Falconer, "Fractal Geometry: Mathematical Foundations and Applications,", John Wiley & Sons, (1990). Google Scholar 
[6] 
Y. A. Kuznetsov, "Elements of Applied Bifurcation Theory,", 2^{nd} edition, 112 (1998). Google Scholar 
[7] 
M. L. Lapidus and C. Pomerance, The Riemann zetafunction and the onedimensional WeylBerry conjecture for fractal drums,, Proc. London Math. Soc. (3), 66 (1993), 41. Google Scholar 
[8] 
P. Mattila, "Geometry of Sets and Measures in Euclidean Spaces. Fractals and Rectifiability,", Cambridge Studies in Advanced Mathematics, 44 (1995). Google Scholar 
[9] 
J. Palis and F. Takens, "Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations. Fractal Dimensions and Infinitely Many Attractors,", Cambridge Studies in Advanced Mathematics, 35 (1993). Google Scholar 
[10] 
M. Pašić, MinkowskiBouligand dimension of solutions of the onedimensional $p$Laplacian,, J. Differential Equations, 190 (2003), 268. doi: 10.1016/S00220396(02)001493. Google Scholar 
[11] 
M. Pašić, D. Žubrinić and V. Županović, Oscillatory and phase dimensions of solutions of some secondorder differential equations,, Bull. Sci. Math., 133 (2009), 859. Google Scholar 
[12] 
L. Perko, "Differential Equations and Dynamical Systems,", 2^{nd} edition, 7 (1996). Google Scholar 
[13] 
C. Tricot, "Curves and Fractal Dimension,", With a foreword by Michel Mendès France, (1995). Google Scholar 
[14] 
S. Wiggins, "Introduction to Applied Nonlinear Dynamical Systems and Chaos,", 2^{nd} edition, 2 (2003). Google Scholar 
[15] 
D. Žubrinić, Analysis of Minkowski content of fractal sets and applications,, Real Anal. Exchange, 31 (): 315. Google Scholar 
[16] 
D. Žubrinić and V. Županović, Fractal dimension in dynamics,, in, (2006), 394. Google Scholar 
[17] 
D. Žubrinić and V. Županović, Poincaré map in fractal analysis of spiral trajectories of planar vector fields,, Bull. Belg. Math. Soc. Simon Stevin, 15 (2008), 947. Google Scholar 
[18] 
D. Žubrinić and V. Županović, Fractal analysis of spiral trajectories of some planar vector fields,, Bull. Sci. Math., 129 (2005), 457. Google Scholar 
[19] 
D. Žubrinić and V. Županović, Fractal analysis of spiral trajectories of some vector fields in $\mathbbR^3$,, C. R. Math. Acad. Sci. Paris, 342 (2006), 959. Google Scholar 
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