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Minimal Følner foliations are amenable
An example of rapid evolution of complex limit cycles
1. | Department of Mathematics and Statistics, McGill University, 805 Sherbrooke W. Montreal, QC H3A 2K6, Canada |
References:
[1] |
V. Arnol'd, S. Guseĭn-Zade and A. Varchenko, "Singularities of Differentiable Maps Vol. II, Monodromy and Asymptotic Integrals," Monographs in Mathematics, 83, Birkhäuser Boston, Inc., Boston, MA, 1988. |
[2] |
G. Binyamini, D. Novikov and S. Yakovenko, On the number of zeros of Abelian integrals, Invent. Math., 181 (2010), 227-289.
doi: 10.1007/s00222-010-0244-0. |
[3] |
L. Carleson and T. W. Gamelin, "Complex Dynamics," Universitext: Tracts in Mathematics, Springer-Verlag, New York, 1993. |
[4] |
E. M. Chirka, "Complex Analytic Sets," Mathematics and its Applications (Soviet Series), 46, Kluwer Academic Publishers Group, Dordrecht, 1989. |
[5] |
J. Conway, "Functions of One Complex Variable," 2nd edition, Graduate Texts in Mathematics, 11, Springer-Verlag, New York-Berlin, 1978. |
[6] |
N. Dimitrov, Rapid evolution of complex limit cycles,, preprint, ().
|
[7] |
N. Dimitrov, Rapid evolution of complex limit cycles, Ph.D. thesis, Cornell University, 2009. |
[8] |
R. C. Gunning and H. Rossi, "Analytic Functions of Several Complex Variables," Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1965. |
[9] |
A. Hatcher, "Algebraic Topology," Cambridge University Press, Cambridge, 2002. |
[10] |
M. W. Hirsch, "Differential Topology," Graduate Texts in Mathematics, Springer-Verlag, New York-Heidelberg, 1976. |
[11] |
Yu. Ilyashenko, Centennial history of Hilbert's 16th problem, Bull. Amer. Math. Soc. (New Series), 39 (2002), 301-354.
doi: 10.1090/S0273-0979-02-00946-1. |
[12] |
Yu. Ilyashenko and S. Yakovenko, "Lectures on Analytic Differential Equations," Graduate Studies in Mathematics, 86, American Mathematical Society, Providence, RI, 2008. |
[13] |
J. Milnor, "Dynamics in One Complex Variable," Third edition, Annals of Mathematics Studies, 160, Princeton University Press, Princeton, New Jersey, 2006. |
[14] |
I. G. Petrovskiĭ and E. M. Landis, On the number of limit cycles of the equation $dw$/$dz=$ $P(z,w)$/$Q(z,w)$, where $P$ and $Q$ are polynomials of 2nd degree, (in Russian), Matem. Sb. N. S., 37 (1955), 209-250. |
[15] |
I. G. Petrovskiĭ and E. M. Landis, On the number of limit cycles of the equation $dw$/$dz=$ $P(z,w)$/$Q(z,w)$, where $P$ and $Q$ are polynomials, (in Russian), Matem. Sb. N. S., 43 (1957), 149-168. |
[16] |
L. S. Pontryagin, On dynamical systems that are close to integrable, Zh. Eksp. Teor. Fiz., 4 (1934), 234-238. |
[17] |
W. Thurston, "Three-Dimensional Geometry and Topology," Vol. I, Princeton Mathematical Series, 35, Princeton University Press, Princeton, New Jersey, 1997. |
show all references
References:
[1] |
V. Arnol'd, S. Guseĭn-Zade and A. Varchenko, "Singularities of Differentiable Maps Vol. II, Monodromy and Asymptotic Integrals," Monographs in Mathematics, 83, Birkhäuser Boston, Inc., Boston, MA, 1988. |
[2] |
G. Binyamini, D. Novikov and S. Yakovenko, On the number of zeros of Abelian integrals, Invent. Math., 181 (2010), 227-289.
doi: 10.1007/s00222-010-0244-0. |
[3] |
L. Carleson and T. W. Gamelin, "Complex Dynamics," Universitext: Tracts in Mathematics, Springer-Verlag, New York, 1993. |
[4] |
E. M. Chirka, "Complex Analytic Sets," Mathematics and its Applications (Soviet Series), 46, Kluwer Academic Publishers Group, Dordrecht, 1989. |
[5] |
J. Conway, "Functions of One Complex Variable," 2nd edition, Graduate Texts in Mathematics, 11, Springer-Verlag, New York-Berlin, 1978. |
[6] |
N. Dimitrov, Rapid evolution of complex limit cycles,, preprint, ().
|
[7] |
N. Dimitrov, Rapid evolution of complex limit cycles, Ph.D. thesis, Cornell University, 2009. |
[8] |
R. C. Gunning and H. Rossi, "Analytic Functions of Several Complex Variables," Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1965. |
[9] |
A. Hatcher, "Algebraic Topology," Cambridge University Press, Cambridge, 2002. |
[10] |
M. W. Hirsch, "Differential Topology," Graduate Texts in Mathematics, Springer-Verlag, New York-Heidelberg, 1976. |
[11] |
Yu. Ilyashenko, Centennial history of Hilbert's 16th problem, Bull. Amer. Math. Soc. (New Series), 39 (2002), 301-354.
doi: 10.1090/S0273-0979-02-00946-1. |
[12] |
Yu. Ilyashenko and S. Yakovenko, "Lectures on Analytic Differential Equations," Graduate Studies in Mathematics, 86, American Mathematical Society, Providence, RI, 2008. |
[13] |
J. Milnor, "Dynamics in One Complex Variable," Third edition, Annals of Mathematics Studies, 160, Princeton University Press, Princeton, New Jersey, 2006. |
[14] |
I. G. Petrovskiĭ and E. M. Landis, On the number of limit cycles of the equation $dw$/$dz=$ $P(z,w)$/$Q(z,w)$, where $P$ and $Q$ are polynomials of 2nd degree, (in Russian), Matem. Sb. N. S., 37 (1955), 209-250. |
[15] |
I. G. Petrovskiĭ and E. M. Landis, On the number of limit cycles of the equation $dw$/$dz=$ $P(z,w)$/$Q(z,w)$, where $P$ and $Q$ are polynomials, (in Russian), Matem. Sb. N. S., 43 (1957), 149-168. |
[16] |
L. S. Pontryagin, On dynamical systems that are close to integrable, Zh. Eksp. Teor. Fiz., 4 (1934), 234-238. |
[17] |
W. Thurston, "Three-Dimensional Geometry and Topology," Vol. I, Princeton Mathematical Series, 35, Princeton University Press, Princeton, New Jersey, 1997. |
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