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Slow motion of particle systems as a limit of a reactiondiffusion equation with halfLaplacian in dimension one
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 
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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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