-
Previous Article
Attractors of Hamilton nonlinear PDEs
- DCDS Home
- This Issue
-
Next Article
An infinite-dimensional weak KAM theory via random variables
Periodic points of latitudinal maps of the $m$-dimensional sphere
1. | Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, Narutowicza 11/12, 80-233 Gdańsk, Poland |
2. | Department of Mathematical Sciences, Indiana University - Purdue University Indianapolis, 402 N. Blackford Street, Indianapolis, IN 46202 |
3. | Sopot, Poland |
References:
[1] |
I. K. Babenko, S. A. Bogatyi, The behavior of the index of periodic points under iterations of a mapping,, Math. USSR Izv., 38 (1992), 1.
|
[2] |
G. Graff and J. Jezierski, On the growth of the number of periodic points for smooth self-maps of a compact manifold,, Proc. Amer. Math. Soc., 135 (2007), 3249.
doi: 10.1090/S0002-9939-07-08836-3. |
[3] |
L. Hernández-Corbato and F. R. Ruiz del Portal, Fixed point indices of planar continuous maps,, Discrete Contin. Dyn. Syst., 35 (2015), 2979.
doi: 10.3934/dcds.2015.35.2979. |
[4] |
B. J. Jiang, Lectures on the Nielsen Fixed Point Theory,, Contemp. Math. 14, 14 (1983).
|
[5] |
V. Kaloshin, Generic diffeomorphisms with superexponential growth of number of periodic orbits,, Comm. Math. Phys., 211 (2000), 253.
doi: 10.1007/s002200050811. |
[6] |
N. G. Lloyd, Degree Theory,, Cambridge Tracts in Mathematics, 73 (1978).
|
[7] |
M. Misiurewicz, Periodic points of latitudinal maps,, J. Fixed Point Theory Appl., 16 (2014), 149.
doi: 10.1007/s11784-014-0195-y. |
[8] |
C. Pugh and M. Shub, Periodic points on the 2-sphere,, Discrete Contin. Dynam. Sys., 34 (2014), 1171.
doi: 10.3934/dcds.2014.34.1171. |
[9] |
M. Shub, Alexander cocycles and dynamics,, Asterisque, 51 (1978), 395.
|
[10] |
M. Shub, All, most, some differentiable dynamical systems,, Proceedings of the International Congress of Mathematicians, (2006), 99.
|
[11] |
M. Shub, Dynamical systems, filtration and entropy,, Bull. Amer. Math. Soc., 80 (1974), 27.
doi: 10.1090/S0002-9904-1974-13344-6. |
[12] |
M. Shub and P. Sullivan, A remark on the Lefschetz fixed point formula for differentiable maps,, Topology, 13 (1974), 189.
doi: 10.1016/0040-9383(74)90009-3. |
show all references
References:
[1] |
I. K. Babenko, S. A. Bogatyi, The behavior of the index of periodic points under iterations of a mapping,, Math. USSR Izv., 38 (1992), 1.
|
[2] |
G. Graff and J. Jezierski, On the growth of the number of periodic points for smooth self-maps of a compact manifold,, Proc. Amer. Math. Soc., 135 (2007), 3249.
doi: 10.1090/S0002-9939-07-08836-3. |
[3] |
L. Hernández-Corbato and F. R. Ruiz del Portal, Fixed point indices of planar continuous maps,, Discrete Contin. Dyn. Syst., 35 (2015), 2979.
doi: 10.3934/dcds.2015.35.2979. |
[4] |
B. J. Jiang, Lectures on the Nielsen Fixed Point Theory,, Contemp. Math. 14, 14 (1983).
|
[5] |
V. Kaloshin, Generic diffeomorphisms with superexponential growth of number of periodic orbits,, Comm. Math. Phys., 211 (2000), 253.
doi: 10.1007/s002200050811. |
[6] |
N. G. Lloyd, Degree Theory,, Cambridge Tracts in Mathematics, 73 (1978).
|
[7] |
M. Misiurewicz, Periodic points of latitudinal maps,, J. Fixed Point Theory Appl., 16 (2014), 149.
doi: 10.1007/s11784-014-0195-y. |
[8] |
C. Pugh and M. Shub, Periodic points on the 2-sphere,, Discrete Contin. Dynam. Sys., 34 (2014), 1171.
doi: 10.3934/dcds.2014.34.1171. |
[9] |
M. Shub, Alexander cocycles and dynamics,, Asterisque, 51 (1978), 395.
|
[10] |
M. Shub, All, most, some differentiable dynamical systems,, Proceedings of the International Congress of Mathematicians, (2006), 99.
|
[11] |
M. Shub, Dynamical systems, filtration and entropy,, Bull. Amer. Math. Soc., 80 (1974), 27.
doi: 10.1090/S0002-9904-1974-13344-6. |
[12] |
M. Shub and P. Sullivan, A remark on the Lefschetz fixed point formula for differentiable maps,, Topology, 13 (1974), 189.
doi: 10.1016/0040-9383(74)90009-3. |
[1] |
Grzegorz Graff, Jerzy Jezierski. Minimization of the number of periodic points for smooth self-maps of closed simply-connected 4-manifolds. Conference Publications, 2011, 2011 (Special) : 523-532. doi: 10.3934/proc.2011.2011.523 |
[2] |
John Erik Fornæss. Periodic points of holomorphic twist maps. Discrete & Continuous Dynamical Systems - A, 2005, 13 (4) : 1047-1056. doi: 10.3934/dcds.2005.13.1047 |
[3] |
Wolfgang Krieger, Kengo Matsumoto. Markov-Dyck shifts, neutral periodic points and topological conjugacy. Discrete & Continuous Dynamical Systems - A, 2019, 39 (1) : 1-18. doi: 10.3934/dcds.2019001 |
[4] |
Daniel Wilczak, Piotr Zgliczyński. Topological method for symmetric periodic orbits for maps with a reversing symmetry. Discrete & Continuous Dynamical Systems - A, 2007, 17 (3) : 629-652. doi: 10.3934/dcds.2007.17.629 |
[5] |
Piotr Oprocha, Paweł Potorski. Topological mixing, knot points and bounds of topological entropy. Discrete & Continuous Dynamical Systems - B, 2015, 20 (10) : 3547-3564. doi: 10.3934/dcdsb.2015.20.3547 |
[6] |
Lluís Alsedà, Sylvie Ruette. On the set of periods of sigma maps of degree 1. Discrete & Continuous Dynamical Systems - A, 2015, 35 (10) : 4683-4734. doi: 10.3934/dcds.2015.35.4683 |
[7] |
Dongkui Ma, Min Wu. Topological pressure and topological entropy of a semigroup of maps. Discrete & Continuous Dynamical Systems - A, 2011, 31 (2) : 545-556. doi: 10.3934/dcds.2011.31.545 |
[8] |
Boris Hasselblatt, Zbigniew Nitecki, James Propp. Topological entropy for nonuniformly continuous maps. Discrete & Continuous Dynamical Systems - A, 2008, 22 (1&2) : 201-213. doi: 10.3934/dcds.2008.22.201 |
[9] |
K. H. Kim, F. W. Roush and J. B. Wagoner. Inert actions on periodic points. Electronic Research Announcements, 1997, 3: 55-62. |
[10] |
Charles Pugh, Michael Shub. Periodic points on the $2$-sphere. Discrete & Continuous Dynamical Systems - A, 2014, 34 (3) : 1171-1182. doi: 10.3934/dcds.2014.34.1171 |
[11] |
Marc Henrard. Homoclinic and multibump solutions for perturbed second order systems using topological degree. Discrete & Continuous Dynamical Systems - A, 1999, 5 (4) : 765-782. doi: 10.3934/dcds.1999.5.765 |
[12] |
Anna Capietto, Walter Dambrosio. A topological degree approach to sublinear systems of second order differential equations. Discrete & Continuous Dynamical Systems - A, 2000, 6 (4) : 861-874. doi: 10.3934/dcds.2000.6.861 |
[13] |
Jian Lu, Huaiyu Jian. Topological degree method for the rotationally symmetric $L_p$-Minkowski problem. Discrete & Continuous Dynamical Systems - A, 2016, 36 (2) : 971-980. doi: 10.3934/dcds.2016.36.971 |
[14] |
Eric Bedford, Kyounghee Kim. Degree growth of matrix inversion: Birational maps of symmetric, cyclic matrices. Discrete & Continuous Dynamical Systems - A, 2008, 21 (4) : 977-1013. doi: 10.3934/dcds.2008.21.977 |
[15] |
Anna Go??biewska, S?awomir Rybicki. Equivariant Conley index versus degree for equivariant gradient maps. Discrete & Continuous Dynamical Systems - S, 2013, 6 (4) : 985-997. doi: 10.3934/dcdss.2013.6.985 |
[16] |
Dante Carrasco-Olivera, Roger Metzger Alvan, Carlos Arnoldo Morales Rojas. Topological entropy for set-valued maps. Discrete & Continuous Dynamical Systems - B, 2015, 20 (10) : 3461-3474. doi: 10.3934/dcdsb.2015.20.3461 |
[17] |
Viviane Baladi, Daniel Smania. Smooth deformations of piecewise expanding unimodal maps. Discrete & Continuous Dynamical Systems - A, 2009, 23 (3) : 685-703. doi: 10.3934/dcds.2009.23.685 |
[18] |
Yong Fang. On smooth conjugacy of expanding maps in higher dimensions. Discrete & Continuous Dynamical Systems - A, 2011, 30 (3) : 687-697. doi: 10.3934/dcds.2011.30.687 |
[19] |
Ralf Spatzier, Lei Yang. Exponential mixing and smooth classification of commuting expanding maps. Journal of Modern Dynamics, 2017, 11: 263-312. doi: 10.3934/jmd.2017012 |
[20] |
Richard Miles, Thomas Ward. Directional uniformities, periodic points, and entropy. Discrete & Continuous Dynamical Systems - B, 2015, 20 (10) : 3525-3545. doi: 10.3934/dcdsb.2015.20.3525 |
2018 Impact Factor: 1.143
Tools
Metrics
Other articles
by authors
[Back to Top]