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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, (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.
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).
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.
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.
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.
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.
|
[8] |
A. Blokh, L. Oversteegen, R. Ptacek and V. Timorin, Dynamical cores of topological polynomials,, Frontiers in complex dynamics, 51 (2014), 27.
doi: 10.1515/9781400851317-005. |
[9] |
A. Blokh, L. Oversteegen, R. Ptacek and V. Timorin, The main cubioid,, Nonlinearity, 27 (2014), 1879.
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.
doi: 10.1007/PL00005568. |
[11] |
C. Carathéodory, Über die Begrenzung einfach zusammenhängender Gebiete (German),, Math. Ann., 73 (1913), 323.
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), 85.
|
[15] |
A. Epstein and M. Yampolsky, Geography of the Cubic Connectedness Locus: Intertwining Surgery,, Ann. Sci. Éc. Norm. Sup., 32 (1999), 151.
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.
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.
|
[18] |
J. Kiwi, Wandering orbit portraits,, Trans. of the Amer. Math. Soc., 354 (2002), 1473.
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.
doi: 10.1016/S0001-8708(03)00144-0. |
[20] |
C. McMullen, The Mandelbrot set is universal,, in: The Mandelbrot Set, 274 (2007), 1.
|
[21] |
J. Milnor, Geometry and dynamics of quadratic rational maps,, Experimental Math., 2 (1993), 37.
doi: 10.1080/10586458.1993.10504267. |
[22] |
J. Milnor, Dynamics in One Complex Variable,, Annals of Mathematical Studies, 160 (2006).
|
[23] |
J. Milnor, Cubic polynomial maps with periodic critical orbit I,, in: Complex Dynamics, (2009), 333.
doi: 10.1201/b10617-13. |
[24] |
J. Milnor and A. Poirier, Hyperbolic components in spaces of polynomial maps,, Contemp. Math., 573 (2012), 183.
doi: 10.1090/conm/573/11428. |
[25] |
J. Milnor and W. Thurston, On iterated maps of the interval,, in Dynamical systems, 1342 (1988), 465.
doi: 10.1007/BFb0082847. |
[26] |
M. Misiurewicz, Horseshoes for mappings of the interval,, Bull. Acad. Pol. Sci., 27 (1979), 167.
|
[27] |
M. Misiurewicz and W. Szlenk, Entropy of piecewise monotone mappings,, Studia Math., 67 (1980), 45.
|
[28] |
C. L. Petersen and T. Lei, Analytic coordinates recording cubic dynamics,, In: Complex Dynamics: Families and Friends, (2009), 413.
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., (). Google Scholar |
[30] |
P. Roesch, Hyperbolic components of polynomials with a fixed critical point of maximal order,, Ann. Sci. école Norm. Sup. (4), 40 (2007), 901.
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, (2009), 3.
doi: 10.1201/b10617-3. |
[32] |
L.-S. Young, On the prevalence of horseshoes,, Trans. Amer. Math. Soc., 263 (1981), 75.
doi: 10.1090/S0002-9947-1981-0590412-0. |
[33] |
S. Zakeri, Dynamics of cubic Siegel polynomials,, Comm. Math. Phys., 206 (1999), 185.
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, (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.
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).
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.
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.
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.
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.
|
[8] |
A. Blokh, L. Oversteegen, R. Ptacek and V. Timorin, Dynamical cores of topological polynomials,, Frontiers in complex dynamics, 51 (2014), 27.
doi: 10.1515/9781400851317-005. |
[9] |
A. Blokh, L. Oversteegen, R. Ptacek and V. Timorin, The main cubioid,, Nonlinearity, 27 (2014), 1879.
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.
doi: 10.1007/PL00005568. |
[11] |
C. Carathéodory, Über die Begrenzung einfach zusammenhängender Gebiete (German),, Math. Ann., 73 (1913), 323.
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), 85.
|
[15] |
A. Epstein and M. Yampolsky, Geography of the Cubic Connectedness Locus: Intertwining Surgery,, Ann. Sci. Éc. Norm. Sup., 32 (1999), 151.
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.
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.
|
[18] |
J. Kiwi, Wandering orbit portraits,, Trans. of the Amer. Math. Soc., 354 (2002), 1473.
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.
doi: 10.1016/S0001-8708(03)00144-0. |
[20] |
C. McMullen, The Mandelbrot set is universal,, in: The Mandelbrot Set, 274 (2007), 1.
|
[21] |
J. Milnor, Geometry and dynamics of quadratic rational maps,, Experimental Math., 2 (1993), 37.
doi: 10.1080/10586458.1993.10504267. |
[22] |
J. Milnor, Dynamics in One Complex Variable,, Annals of Mathematical Studies, 160 (2006).
|
[23] |
J. Milnor, Cubic polynomial maps with periodic critical orbit I,, in: Complex Dynamics, (2009), 333.
doi: 10.1201/b10617-13. |
[24] |
J. Milnor and A. Poirier, Hyperbolic components in spaces of polynomial maps,, Contemp. Math., 573 (2012), 183.
doi: 10.1090/conm/573/11428. |
[25] |
J. Milnor and W. Thurston, On iterated maps of the interval,, in Dynamical systems, 1342 (1988), 465.
doi: 10.1007/BFb0082847. |
[26] |
M. Misiurewicz, Horseshoes for mappings of the interval,, Bull. Acad. Pol. Sci., 27 (1979), 167.
|
[27] |
M. Misiurewicz and W. Szlenk, Entropy of piecewise monotone mappings,, Studia Math., 67 (1980), 45.
|
[28] |
C. L. Petersen and T. Lei, Analytic coordinates recording cubic dynamics,, In: Complex Dynamics: Families and Friends, (2009), 413.
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., (). Google Scholar |
[30] |
P. Roesch, Hyperbolic components of polynomials with a fixed critical point of maximal order,, Ann. Sci. école Norm. Sup. (4), 40 (2007), 901.
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, (2009), 3.
doi: 10.1201/b10617-3. |
[32] |
L.-S. Young, On the prevalence of horseshoes,, Trans. Amer. Math. Soc., 263 (1981), 75.
doi: 10.1090/S0002-9947-1981-0590412-0. |
[33] |
S. Zakeri, Dynamics of cubic Siegel polynomials,, Comm. Math. Phys., 206 (1999), 185.
doi: 10.1007/s002200050702. |
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