American Institute of Mathematical Sciences

March  2003, 9(2): 497-503. doi: 10.3934/dcds.2003.9.497

Accumulation points of flows on the Klein bottle

 1 Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, C/ Alfonso XIII, 52. 30203-Cartagena, Spain

Received  October 2001 Revised  March 2002 Published  December 2002

The aim of this paper is to give a topological characterization of the sets that can be $\omega$-limit of continuous dynamical systems in the Klein bottle. This problem has been recently solved for the case of the projective plane answering a problem proposed by Anosov.
Citation: Gabriel Soler López. Accumulation points of flows on the Klein bottle. Discrete & Continuous Dynamical Systems - A, 2003, 9 (2) : 497-503. doi: 10.3934/dcds.2003.9.497
 [1] Artem Dudko. Computability of the Julia set. Nonrecurrent critical orbits. Discrete & Continuous Dynamical Systems - A, 2014, 34 (7) : 2751-2778. doi: 10.3934/dcds.2014.34.2751 [2] Jingxian Sun, Shouchuan Hu. Flow-invariant sets and critical point theory. Discrete & Continuous Dynamical Systems - A, 2003, 9 (2) : 483-496. doi: 10.3934/dcds.2003.9.483 [3] Tatiane C. Batista, Juliano S. Gonschorowski, Fábio A. Tal. Density of the set of endomorphisms with a maximizing measure supported on a periodic orbit. Discrete & Continuous Dynamical Systems - A, 2015, 35 (8) : 3315-3326. doi: 10.3934/dcds.2015.35.3315 [4] Changjing Zhuge, Xiaojuan Sun, Jinzhi Lei. On positive solutions and the Omega limit set for a class of delay differential equations. Discrete & Continuous Dynamical Systems - B, 2013, 18 (9) : 2487-2503. doi: 10.3934/dcdsb.2013.18.2487 [5] Yakov Krasnov, Alexander Kononovich, Grigory Osharovich. On a structure of the fixed point set of homogeneous maps. Discrete & Continuous Dynamical Systems - S, 2013, 6 (4) : 1017-1027. doi: 10.3934/dcdss.2013.6.1017 [6] Antonio Ambrosetti, Massimiliano Berti. Applications of critical point theory to homoclinics and complex dynamics. Conference Publications, 1998, 1998 (Special) : 72-78. doi: 10.3934/proc.1998.1998.72 [7] Anna Maria Candela, Giuliana Palmieri. Some abstract critical point theorems and applications. Conference Publications, 2009, 2009 (Special) : 133-142. doi: 10.3934/proc.2009.2009.133 [8] Domingo González, Gamaliel Blé. Core entropy of polynomials with a critical point of maximal order. Discrete & Continuous Dynamical Systems - A, 2019, 39 (1) : 115-130. doi: 10.3934/dcds.2019005 [9] Matthias Rumberger. Lyapunov exponents on the orbit space. Discrete & Continuous Dynamical Systems - A, 2001, 7 (1) : 91-113. doi: 10.3934/dcds.2001.7.91 [10] Stefano Galatolo. Orbit complexity and data compression. Discrete & Continuous Dynamical Systems - A, 2001, 7 (3) : 477-486. doi: 10.3934/dcds.2001.7.477 [11] Shiqiu Liu, Frédérique Oggier. On applications of orbit codes to storage. Advances in Mathematics of Communications, 2016, 10 (1) : 113-130. doi: 10.3934/amc.2016.10.113 [12] Peng Sun. Minimality and gluing orbit property. Discrete & Continuous Dynamical Systems - A, 2019, 39 (7) : 4041-4056. doi: 10.3934/dcds.2019162 [13] Tiphaine Jézéquel, Patrick Bernard, Eric Lombardi. Homoclinic orbits with many loops near a $0^2 i\omega$ resonant fixed point of Hamiltonian systems. Discrete & Continuous Dynamical Systems - A, 2016, 36 (6) : 3153-3225. doi: 10.3934/dcds.2016.36.3153 [14] Heide Gluesing-Luerssen, Katherine Morrison, Carolyn Troha. Cyclic orbit codes and stabilizer subfields. Advances in Mathematics of Communications, 2015, 9 (2) : 177-197. doi: 10.3934/amc.2015.9.177 [15] Andres del Junco, Daniel J. Rudolph, Benjamin Weiss. Measured topological orbit and Kakutani equivalence. Discrete & Continuous Dynamical Systems - S, 2009, 2 (2) : 221-238. doi: 10.3934/dcdss.2009.2.221 [16] François Delarue, Franco Flandoli. The transition point in the zero noise limit for a 1D Peano example. Discrete & Continuous Dynamical Systems - A, 2014, 34 (10) : 4071-4083. doi: 10.3934/dcds.2014.34.4071 [17] Urszula Foryś, Yuri Kheifetz, Yuri Kogan. Critical-Point Analysis For Three-Variable Cancer Angiogenesis Models. Mathematical Biosciences & Engineering, 2005, 2 (3) : 511-525. doi: 10.3934/mbe.2005.2.511 [18] Salvatore A. Marano, Sunra Mosconi. Non-smooth critical point theory on closed convex sets. Communications on Pure & Applied Analysis, 2014, 13 (3) : 1187-1202. doi: 10.3934/cpaa.2014.13.1187 [19] Mohameden Ahmedou, Mohamed Ben Ayed, Marcello Lucia. On a resonant mean field type equation: A "critical point at Infinity" approach. Discrete & Continuous Dynamical Systems - A, 2017, 37 (4) : 1789-1818. doi: 10.3934/dcds.2017075 [20] Kazuo Aoki, Yoshiaki Abe. Stagnation-point flow of a rarefied gas impinging obliquely on a plane wall. Kinetic & Related Models, 2011, 4 (4) : 935-954. doi: 10.3934/krm.2011.4.935

2018 Impact Factor: 1.143