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On the Fibonacci complex dynamical systems
1. | Normandy university,Department of Mathematics, University of Rouen, LMRS, UMR 60 85, Avenue de l'Universite, BP.12, 76801, Saint Etienne du Rouvray, France |
2. | Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, São Paulo, SP, Brazil |
3. | Departamento de Matemática, Universidade Estadual Paulista, Rua Cristovão Colombo, 2265, CEP 15054-0000, São José do Rio Preto-SP, Brazil |
4. | Université Paris-Est, UMR 8050, CNRS, UPEMLV, F-77454,, Marne-la-Vallée, France |
References:
[1] |
L. V. Ahlfors, Lectures on Quasiconformal Mappings, Second edition, American Mathematical Society, Providence, 2006.
doi: 10.1090/ulect/038. |
[2] |
E. Bedford and J. Smillie, Polynomial diffeomorphisms of $C^2$: Currents, equilibrium measure and hyperbolicity, Invent. Math., 103 (1991), 69-99.
doi: 10.1007/BF01239509. |
[3] |
P. Berger, Persistence of laminations, Bull. Braz. Math. Soc. (N.S.), 41 (2010), 259-319.
doi: 10.1007/s00574-010-0013-0. |
[4] |
L. Carleson and T. W. Gamelin, Complex Dynamics, Springer-Verlag, New York, 1993.
doi: 10.1007/978-1-4612-4364-9 . |
[5] |
E. H. El Abdalaoui and A. Messaoudi, On the spectrum of stochastic perturbations of the shift and Julia sets, Fundamenta Mathematicae, 218 (2012), 47-68.
doi: 10.4064/fm218-1-3. |
[6] |
E. de Faria and W. de Melo, Mathematical Tools for One-Dimensional Dynamics, Cambridge University Press, Cambridge, 2008.
doi: 10.1017/cbo9780511755231. |
[7] |
J. E. Fornæss and N. Sibony, Complex Hénon mappings in $C^2$ and Fatou-Bieberbach domains, Duke Math. J., 65 (1992), 345-380.
doi: 10.1215/S0012-7094-92-06515-X. |
[8] |
V. Guedj, Dynamics of quadratic polynomial mappings of $\mathbbC^2$, Michigan Math. J., 52 (2004), 627-648.
doi: 10.1307/mmj/1100623417. |
[9] |
V. Guedj, Propriétés ergodiques des applications rationnelles, in Panor. Synthèses, 30 (2010), 97-202. |
[10] |
V. Guillemin and A. Pollack, Differential Topology, AMS Chelsea Publishing, Providence, 2010. |
[11] |
S. L. Hruska and R. Roeder, Topology of Fatou components for endomorphisms of $\mathbb{CP}^k$: Linking with the Green's current, Fund. Math., 210 (2010), 73-98.
doi: 10.4064/fm210-1-4. |
[12] |
J. H. Hubbard and R. W. Oberste-Vorth, Hénon mappings in the complex domain. II. Projective and inductive limits of polynomials, in NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 464 (1995), 89-132. |
[13] |
A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, Cambridge, 1995.
doi: 10.1017/cbo9780511809187. |
[14] |
P. R. Killeen and T. J. Taylor, A stochastic adding machine and complex dynamics, Nonlinearity, 13 (2000), 1889-1903.
doi: 10.1088/0951-7715/13/6/302. |
[15] |
A. Messaoudi and D. Smania, Eigenvalues of Fibonacci stochastic adding machine, Stoch. Dyn., 10 (2010), 291-313.
doi: 10.1142/S0219493710002966. |
[16] |
S. Morosawa, Y. Nishimura, M. Taniguchi and T. Ueda, Holomorphic Dynamics, Cambridge University Press, Cambridge, 2000.
doi: d.doi.org/10.1017/s0143385700001036. |
[17] |
C. Robinson, An Introduction to Dynamical Systems, Continuous and Discrete, Second edition, American Mathematical Society, Providence, 2012. |
[18] |
D. Ruelle, Elements of Differentiable Dynamics and Bifurcation Theory, Academic Press Inc., Boston, 1989. |
show all references
References:
[1] |
L. V. Ahlfors, Lectures on Quasiconformal Mappings, Second edition, American Mathematical Society, Providence, 2006.
doi: 10.1090/ulect/038. |
[2] |
E. Bedford and J. Smillie, Polynomial diffeomorphisms of $C^2$: Currents, equilibrium measure and hyperbolicity, Invent. Math., 103 (1991), 69-99.
doi: 10.1007/BF01239509. |
[3] |
P. Berger, Persistence of laminations, Bull. Braz. Math. Soc. (N.S.), 41 (2010), 259-319.
doi: 10.1007/s00574-010-0013-0. |
[4] |
L. Carleson and T. W. Gamelin, Complex Dynamics, Springer-Verlag, New York, 1993.
doi: 10.1007/978-1-4612-4364-9 . |
[5] |
E. H. El Abdalaoui and A. Messaoudi, On the spectrum of stochastic perturbations of the shift and Julia sets, Fundamenta Mathematicae, 218 (2012), 47-68.
doi: 10.4064/fm218-1-3. |
[6] |
E. de Faria and W. de Melo, Mathematical Tools for One-Dimensional Dynamics, Cambridge University Press, Cambridge, 2008.
doi: 10.1017/cbo9780511755231. |
[7] |
J. E. Fornæss and N. Sibony, Complex Hénon mappings in $C^2$ and Fatou-Bieberbach domains, Duke Math. J., 65 (1992), 345-380.
doi: 10.1215/S0012-7094-92-06515-X. |
[8] |
V. Guedj, Dynamics of quadratic polynomial mappings of $\mathbbC^2$, Michigan Math. J., 52 (2004), 627-648.
doi: 10.1307/mmj/1100623417. |
[9] |
V. Guedj, Propriétés ergodiques des applications rationnelles, in Panor. Synthèses, 30 (2010), 97-202. |
[10] |
V. Guillemin and A. Pollack, Differential Topology, AMS Chelsea Publishing, Providence, 2010. |
[11] |
S. L. Hruska and R. Roeder, Topology of Fatou components for endomorphisms of $\mathbb{CP}^k$: Linking with the Green's current, Fund. Math., 210 (2010), 73-98.
doi: 10.4064/fm210-1-4. |
[12] |
J. H. Hubbard and R. W. Oberste-Vorth, Hénon mappings in the complex domain. II. Projective and inductive limits of polynomials, in NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 464 (1995), 89-132. |
[13] |
A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, Cambridge, 1995.
doi: 10.1017/cbo9780511809187. |
[14] |
P. R. Killeen and T. J. Taylor, A stochastic adding machine and complex dynamics, Nonlinearity, 13 (2000), 1889-1903.
doi: 10.1088/0951-7715/13/6/302. |
[15] |
A. Messaoudi and D. Smania, Eigenvalues of Fibonacci stochastic adding machine, Stoch. Dyn., 10 (2010), 291-313.
doi: 10.1142/S0219493710002966. |
[16] |
S. Morosawa, Y. Nishimura, M. Taniguchi and T. Ueda, Holomorphic Dynamics, Cambridge University Press, Cambridge, 2000.
doi: d.doi.org/10.1017/s0143385700001036. |
[17] |
C. Robinson, An Introduction to Dynamical Systems, Continuous and Discrete, Second edition, American Mathematical Society, Providence, 2012. |
[18] |
D. Ruelle, Elements of Differentiable Dynamics and Bifurcation Theory, Academic Press Inc., Boston, 1989. |
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