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Bifurcation and one-sign solutions of the $p$-Laplacian involving a nonlinearity with zeros
Periodic and eventually periodic points of affine infra-nilmanifold endomorphisms
1. | KU Leuven Kulak, E. Sabbelaan 53, 8500 Kortrijk, Belgium |
References:
[1] |
D. V. Anosov, Geodesic flow on closed Riemannian manifolds with negative curvature, Trudy Mat. Inst. Steklov., 90 (1967), 209pp. |
[2] |
K. Dekimpe, Almost-Bieberbach Groups: Affine and Polynomial Structures, Lect. Notes in Math., 1639, Springer-Verlag, 1996. |
[3] |
K. Dekimpe, What an infra-nilmanifold endomorphism really should be..., Topological Methods in Nonlinear Analysis, 40 (2012), 111-136. |
[4] |
K. Dekimpe and J. Deré, Expanding maps and non-trivial self-covers on infra-nilmanifolds, Topological Methods in Nonlinear Analysis, 47 (2016), 347-368. |
[5] |
R. L. Devaney, An Introduction to Chaotic Dynamical Systems, Addison-Wesley Studies in Nonlinearity $2^{nd}$ edition, Addison-Wesley Publishing Company, Advanced Book Program, Redwood City, CA, 1989, Studies in Nonlinearity. Westview Press, Boulder, CO, 2003. |
[6] |
M. Gromov, Groups of polynomial growth and expanding maps, Institut des Hautes Études Scientifiques, 53 (1981), 53-73. |
[7] |
K. Y. Ha, H. J. Kim and J. B. Lee, Eventually periodic points of infra-nil endomorphisms, Fixed Point Theory Appl., (2010), Art. ID 721736, 15pp. |
[8] |
K. B. Lee, Maps on infra-nilmanifolds, Pacific J. Math., 168 (1995), 157-166.
doi: 10.2140/pjm.1995.168.157. |
[9] |
A. Manning, There are no new Anosov diffeomorphisms on tori, Amer. J. Math., 96 (1974), 422-429.
doi: 10.2307/2373551. |
[10] |
J. R. Munkres, Topology: A First Course, $2^{nd}$ edition, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1975. |
[11] |
S. E. Newhouse, On codimension one Anosov diffeomorphisms, Amer. J. Math, 92 (1970), 761-770.
doi: 10.2307/2373372. |
[12] |
D. Segal, Polycyclic Groups, Cambridge University Press, 1983.
doi: 10.1017/CBO9780511565953. |
[13] |
M. Shub, Endomorphisms of compact differentiable manifolds, Amer. J. Math, 91 (1969), 175-199.
doi: 10.2307/2373276. |
[14] |
S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc., 73 (1967), 747-817.
doi: 10.1090/S0002-9904-1967-11798-1. |
show all references
References:
[1] |
D. V. Anosov, Geodesic flow on closed Riemannian manifolds with negative curvature, Trudy Mat. Inst. Steklov., 90 (1967), 209pp. |
[2] |
K. Dekimpe, Almost-Bieberbach Groups: Affine and Polynomial Structures, Lect. Notes in Math., 1639, Springer-Verlag, 1996. |
[3] |
K. Dekimpe, What an infra-nilmanifold endomorphism really should be..., Topological Methods in Nonlinear Analysis, 40 (2012), 111-136. |
[4] |
K. Dekimpe and J. Deré, Expanding maps and non-trivial self-covers on infra-nilmanifolds, Topological Methods in Nonlinear Analysis, 47 (2016), 347-368. |
[5] |
R. L. Devaney, An Introduction to Chaotic Dynamical Systems, Addison-Wesley Studies in Nonlinearity $2^{nd}$ edition, Addison-Wesley Publishing Company, Advanced Book Program, Redwood City, CA, 1989, Studies in Nonlinearity. Westview Press, Boulder, CO, 2003. |
[6] |
M. Gromov, Groups of polynomial growth and expanding maps, Institut des Hautes Études Scientifiques, 53 (1981), 53-73. |
[7] |
K. Y. Ha, H. J. Kim and J. B. Lee, Eventually periodic points of infra-nil endomorphisms, Fixed Point Theory Appl., (2010), Art. ID 721736, 15pp. |
[8] |
K. B. Lee, Maps on infra-nilmanifolds, Pacific J. Math., 168 (1995), 157-166.
doi: 10.2140/pjm.1995.168.157. |
[9] |
A. Manning, There are no new Anosov diffeomorphisms on tori, Amer. J. Math., 96 (1974), 422-429.
doi: 10.2307/2373551. |
[10] |
J. R. Munkres, Topology: A First Course, $2^{nd}$ edition, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1975. |
[11] |
S. E. Newhouse, On codimension one Anosov diffeomorphisms, Amer. J. Math, 92 (1970), 761-770.
doi: 10.2307/2373372. |
[12] |
D. Segal, Polycyclic Groups, Cambridge University Press, 1983.
doi: 10.1017/CBO9780511565953. |
[13] |
M. Shub, Endomorphisms of compact differentiable manifolds, Amer. J. Math, 91 (1969), 175-199.
doi: 10.2307/2373276. |
[14] |
S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc., 73 (1967), 747-817.
doi: 10.1090/S0002-9904-1967-11798-1. |
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