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Laminations from the main cubioid
1. | Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294-1170 |
2. | Faculty of Mathematics, Laboratory of Algebraic Geometry and its Applications, National Research University Higher School of Economics, Vavilova St. 7, 112312 Moscow, Russian Federation, Russian Federation |
References:
[1] |
L. Alseda, J. Llibre and M. Misiurewicz, Combinatorial Dynamics and Entropy in Dimension One, World Scientific (Advanced Series in Nonlinear Dynamics, vol. 5), Second Edition, 2000.
doi: 10.1142/4205. |
[2] |
A. Blokh, C. Curry and L. Oversteegen, Locally connected models for Julia sets, Advances in Mathematics, 226 (2011), 1621-1661.
doi: 10.1016/j.aim.2010.08.011. |
[3] |
A. Blokh, R. Fokkink, J. Mayer, L. Oversteegen and E. Tymchatyn, Fixed point theorems in plane continua with applications, Memoirs of the American Mathematical Society, 224 (2013), xiv+97 pp.
doi: 10.1090/S0065-9266-2012-00671-X. |
[4] |
A. Blokh and G. Levin, Growing trees, laminations and the dynamics on the Julia set, Ergod. Th. and Dynam. Sys., 22 (2002), 63-97.
doi: 10.1017/S0143385702000032. |
[5] |
A. Blokh, J. Malaugh, J. Mayer, L. Oversteegen and D. Parris, Rotational subsets of the circle under $z^n$, Topology and its Appl., 153 (2006), 1540-1570.
doi: 10.1016/j.topol.2005.04.010. |
[6] |
A. Blokh, D. Mimbs, L. Oversteegen and K. Valkenburg, Laminations in the language of leaves, Trans. of the Amer. Math. Soc., 365 (2013), 5367-5391.
doi: 10.1090/S0002-9947-2013-05809-6. |
[7] |
A. Blokh and L. Oversteegen, {Monotone images of Cremer Julia sets, Houston Journal of Mathematics, 36 (2010), 469-476. |
[8] |
A. Blokh, L. Oversteegen, R. Ptacek and V. Timorin, Dynamical cores of topological polynomials, Frontiers in complex dynamics, Princeton Math. Ser., Princeton Univ. Press, Princeton, NJ, 51 (2014), 27-48.
doi: 10.1515/9781400851317-005. |
[9] |
A. Blokh, L. Oversteegen, R. Ptacek and V. Timorin, The main cubioid, Nonlinearity, 27 (2014), 1879-1897.
doi: 10.1088/0951-7715/27/8/1879. |
[10] |
X. Buff and C. Henriksen, Julia Sets in Parameter Spaces, Commun. Math. Phys., 220 (2001), 333-375.
doi: 10.1007/PL00005568. |
[11] |
C. Carathéodory, Über die Begrenzung einfach zusammenhängender Gebiete (German), Math. Ann., 73 (1913), 323-370.
doi: 10.1007/BF01456699. |
[12] |
L. Carleson and T. W. Gamelin, Complex Dynamics, Springer, 1993.
doi: 10.1007/978-1-4612-4364-9. |
[13] |
A. Douady and J. H. Hubbard, Étude dynamique des polynômes complexes I, Publications Mathématiques d'Orsay, 1984. |
[14] |
A. Douady and J. H. Hubbard, Étude dynamique des polynômes complexes II, Publications Mathématiques d'Orsay, 85-04, 1985. |
[15] |
A. Epstein and M. Yampolsky, Geography of the Cubic Connectedness Locus: Intertwining Surgery, Ann. Sci. Éc. Norm. Sup., 32 (1999), 151-185.
doi: 10.1016/S0012-9593(99)80013-5. |
[16] |
T. Gauthier, Higher bifurcation currents, neutral cycles, and the Mandelbrot set, Indiana Univ. Math. J., 63 (2014), 917-937.
doi: 10.1512/iumj.2014.63.5328. |
[17] |
L. Goldberg and J. Milnor, Fixed points of polynomial maps. II. Fixed point portraits, Ann. Sci. École Norm. Sup. (4), 26 (1993), 51-98. |
[18] |
J. Kiwi, Wandering orbit portraits, Trans. of the Amer. Math. Soc., 354 (2002), 1473-1485.
doi: 10.1090/S0002-9947-01-02896-3. |
[19] |
J. Kiwi, $\mathbb R$eal laminations and the topological dynamics of complex polynomials, Advances in Mathematics, 184 (2004), 207-267.
doi: 10.1016/S0001-8708(03)00144-0. |
[20] |
C. McMullen, The Mandelbrot set is universal, in: The Mandelbrot Set, Theme and Variations, ed. T. Lei, Cambridge U.K. Cambridge Univ. Press. Revised, 274 (2007), 1-17. |
[21] |
J. Milnor, Geometry and dynamics of quadratic rational maps, Experimental Math., 2 (1993), 37-83.
doi: 10.1080/10586458.1993.10504267. |
[22] |
J. Milnor, Dynamics in One Complex Variable, Annals of Mathematical Studies, 160, Princeton, 2006. |
[23] |
J. Milnor, Cubic polynomial maps with periodic critical orbit I, in: Complex Dynamics, Families and Friends, ed. D. Schleicher, A.K. Peters (2009), 333-411.
doi: 10.1201/b10617-13. |
[24] |
J. Milnor and A. Poirier, Hyperbolic components in spaces of polynomial maps, Contemp. Math., Conformal dynamics and hyperbolic geometry, Amer. Math. Soc., Providence, RI, 573 (2012), 183-232. arXiv:math/9202210
doi: 10.1090/conm/573/11428. |
[25] |
J. Milnor and W. Thurston, On iterated maps of the interval, in Dynamical systems, Lecture Notes in Math., 1342, Springer, Berlin, (1988), 465-563.
doi: 10.1007/BFb0082847. |
[26] |
M. Misiurewicz, Horseshoes for mappings of the interval, Bull. Acad. Pol. Sci., Ser. sci. math., astr. et phys., 27 (1979), 167-169. |
[27] |
M. Misiurewicz and W. Szlenk, Entropy of piecewise monotone mappings, Studia Math., 67 (1980), 45-63. |
[28] |
C. L. Petersen and T. Lei, Analytic coordinates recording cubic dynamics, In: Complex Dynamics: Families and Friends, ed. Dierk Schleicher, Wellesley Massachusetts: A. K. Peters, Limited, (2009), 413-449.
doi: 10.1201/b10617-14. |
[29] |
C. L. Petersen, P. Roesch and T. Lei, Parabolic slices on the boundary of $\mathcal H$,, work in progress., ().
|
[30] |
P. Roesch, Hyperbolic components of polynomials with a fixed critical point of maximal order, Ann. Sci. école Norm. Sup. (4), 40 (2007), 901-949.
doi: 10.1016/j.ansens.2007.10.001. |
[31] |
W. Thurston, On the geometry and dynamics of iterated rational maps, in: Complex dynamics: Families and Friends, ed. by D. Schleicher, A K Peters, (2009), 3-137.
doi: 10.1201/b10617-3. |
[32] |
L.-S. Young, On the prevalence of horseshoes, Trans. Amer. Math. Soc., 263 (1981), 75-88.
doi: 10.1090/S0002-9947-1981-0590412-0. |
[33] |
S. Zakeri, Dynamics of cubic Siegel polynomials, Comm. Math. Phys., 206 (1999), 185-233.
doi: 10.1007/s002200050702. |
show all references
References:
[1] |
L. Alseda, J. Llibre and M. Misiurewicz, Combinatorial Dynamics and Entropy in Dimension One, World Scientific (Advanced Series in Nonlinear Dynamics, vol. 5), Second Edition, 2000.
doi: 10.1142/4205. |
[2] |
A. Blokh, C. Curry and L. Oversteegen, Locally connected models for Julia sets, Advances in Mathematics, 226 (2011), 1621-1661.
doi: 10.1016/j.aim.2010.08.011. |
[3] |
A. Blokh, R. Fokkink, J. Mayer, L. Oversteegen and E. Tymchatyn, Fixed point theorems in plane continua with applications, Memoirs of the American Mathematical Society, 224 (2013), xiv+97 pp.
doi: 10.1090/S0065-9266-2012-00671-X. |
[4] |
A. Blokh and G. Levin, Growing trees, laminations and the dynamics on the Julia set, Ergod. Th. and Dynam. Sys., 22 (2002), 63-97.
doi: 10.1017/S0143385702000032. |
[5] |
A. Blokh, J. Malaugh, J. Mayer, L. Oversteegen and D. Parris, Rotational subsets of the circle under $z^n$, Topology and its Appl., 153 (2006), 1540-1570.
doi: 10.1016/j.topol.2005.04.010. |
[6] |
A. Blokh, D. Mimbs, L. Oversteegen and K. Valkenburg, Laminations in the language of leaves, Trans. of the Amer. Math. Soc., 365 (2013), 5367-5391.
doi: 10.1090/S0002-9947-2013-05809-6. |
[7] |
A. Blokh and L. Oversteegen, {Monotone images of Cremer Julia sets, Houston Journal of Mathematics, 36 (2010), 469-476. |
[8] |
A. Blokh, L. Oversteegen, R. Ptacek and V. Timorin, Dynamical cores of topological polynomials, Frontiers in complex dynamics, Princeton Math. Ser., Princeton Univ. Press, Princeton, NJ, 51 (2014), 27-48.
doi: 10.1515/9781400851317-005. |
[9] |
A. Blokh, L. Oversteegen, R. Ptacek and V. Timorin, The main cubioid, Nonlinearity, 27 (2014), 1879-1897.
doi: 10.1088/0951-7715/27/8/1879. |
[10] |
X. Buff and C. Henriksen, Julia Sets in Parameter Spaces, Commun. Math. Phys., 220 (2001), 333-375.
doi: 10.1007/PL00005568. |
[11] |
C. Carathéodory, Über die Begrenzung einfach zusammenhängender Gebiete (German), Math. Ann., 73 (1913), 323-370.
doi: 10.1007/BF01456699. |
[12] |
L. Carleson and T. W. Gamelin, Complex Dynamics, Springer, 1993.
doi: 10.1007/978-1-4612-4364-9. |
[13] |
A. Douady and J. H. Hubbard, Étude dynamique des polynômes complexes I, Publications Mathématiques d'Orsay, 1984. |
[14] |
A. Douady and J. H. Hubbard, Étude dynamique des polynômes complexes II, Publications Mathématiques d'Orsay, 85-04, 1985. |
[15] |
A. Epstein and M. Yampolsky, Geography of the Cubic Connectedness Locus: Intertwining Surgery, Ann. Sci. Éc. Norm. Sup., 32 (1999), 151-185.
doi: 10.1016/S0012-9593(99)80013-5. |
[16] |
T. Gauthier, Higher bifurcation currents, neutral cycles, and the Mandelbrot set, Indiana Univ. Math. J., 63 (2014), 917-937.
doi: 10.1512/iumj.2014.63.5328. |
[17] |
L. Goldberg and J. Milnor, Fixed points of polynomial maps. II. Fixed point portraits, Ann. Sci. École Norm. Sup. (4), 26 (1993), 51-98. |
[18] |
J. Kiwi, Wandering orbit portraits, Trans. of the Amer. Math. Soc., 354 (2002), 1473-1485.
doi: 10.1090/S0002-9947-01-02896-3. |
[19] |
J. Kiwi, $\mathbb R$eal laminations and the topological dynamics of complex polynomials, Advances in Mathematics, 184 (2004), 207-267.
doi: 10.1016/S0001-8708(03)00144-0. |
[20] |
C. McMullen, The Mandelbrot set is universal, in: The Mandelbrot Set, Theme and Variations, ed. T. Lei, Cambridge U.K. Cambridge Univ. Press. Revised, 274 (2007), 1-17. |
[21] |
J. Milnor, Geometry and dynamics of quadratic rational maps, Experimental Math., 2 (1993), 37-83.
doi: 10.1080/10586458.1993.10504267. |
[22] |
J. Milnor, Dynamics in One Complex Variable, Annals of Mathematical Studies, 160, Princeton, 2006. |
[23] |
J. Milnor, Cubic polynomial maps with periodic critical orbit I, in: Complex Dynamics, Families and Friends, ed. D. Schleicher, A.K. Peters (2009), 333-411.
doi: 10.1201/b10617-13. |
[24] |
J. Milnor and A. Poirier, Hyperbolic components in spaces of polynomial maps, Contemp. Math., Conformal dynamics and hyperbolic geometry, Amer. Math. Soc., Providence, RI, 573 (2012), 183-232. arXiv:math/9202210
doi: 10.1090/conm/573/11428. |
[25] |
J. Milnor and W. Thurston, On iterated maps of the interval, in Dynamical systems, Lecture Notes in Math., 1342, Springer, Berlin, (1988), 465-563.
doi: 10.1007/BFb0082847. |
[26] |
M. Misiurewicz, Horseshoes for mappings of the interval, Bull. Acad. Pol. Sci., Ser. sci. math., astr. et phys., 27 (1979), 167-169. |
[27] |
M. Misiurewicz and W. Szlenk, Entropy of piecewise monotone mappings, Studia Math., 67 (1980), 45-63. |
[28] |
C. L. Petersen and T. Lei, Analytic coordinates recording cubic dynamics, In: Complex Dynamics: Families and Friends, ed. Dierk Schleicher, Wellesley Massachusetts: A. K. Peters, Limited, (2009), 413-449.
doi: 10.1201/b10617-14. |
[29] |
C. L. Petersen, P. Roesch and T. Lei, Parabolic slices on the boundary of $\mathcal H$,, work in progress., ().
|
[30] |
P. Roesch, Hyperbolic components of polynomials with a fixed critical point of maximal order, Ann. Sci. école Norm. Sup. (4), 40 (2007), 901-949.
doi: 10.1016/j.ansens.2007.10.001. |
[31] |
W. Thurston, On the geometry and dynamics of iterated rational maps, in: Complex dynamics: Families and Friends, ed. by D. Schleicher, A K Peters, (2009), 3-137.
doi: 10.1201/b10617-3. |
[32] |
L.-S. Young, On the prevalence of horseshoes, Trans. Amer. Math. Soc., 263 (1981), 75-88.
doi: 10.1090/S0002-9947-1981-0590412-0. |
[33] |
S. Zakeri, Dynamics of cubic Siegel polynomials, Comm. Math. Phys., 206 (1999), 185-233.
doi: 10.1007/s002200050702. |
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