
Previous Article
Asymptotics of the solitary waves for the generalized KadomtsevPetviashvili equations
 DCDS Home
 This Issue

Next Article
Perturbations of embedded eigenvalues for the bilaplacian on a cylinder
Discrete and continuous spectra on laminations over AubryMather sets
1.  LAGA, CNRS UMR 7539, Université Paris 13, Villetaneuse 93430 
The answer will essentially depend on the number of orbits of gaps in the AubryMather set. More precisely, if the AubryMather set has exactly one orbit of gaps and is hyperbolic then the special flow over it with any smooth ceiling function will be conjugate to a suspension with a constant ceiling function, failing hence to be weak mixing or even topologically weak mixing. To the contrary, if the AubryMather set has more than one orbit of gaps with at least two in a general position then the special flow over it will in general be weak mixing.
[1] 
Kaizhi Wang, Lin Wang, Jun Yan. AubryMather theory for contact Hamiltonian systems II. Discrete & Continuous Dynamical Systems, 2022, 42 (2) : 555595. doi: 10.3934/dcds.2021128 
[2] 
Ugo Bessi. Viscous AubryMather theory and the Vlasov equation. Discrete & Continuous Dynamical Systems, 2014, 34 (2) : 379420. doi: 10.3934/dcds.2014.34.379 
[3] 
Hans Koch, Rafael De La Llave, Charles Radin. AubryMather theory for functions on lattices. Discrete & Continuous Dynamical Systems, 1997, 3 (1) : 135151. doi: 10.3934/dcds.1997.3.135 
[4] 
Fabio Camilli, Annalisa Cesaroni. A note on singular perturbation problems via AubryMather theory. Discrete & Continuous Dynamical Systems, 2007, 17 (4) : 807819. doi: 10.3934/dcds.2007.17.807 
[5] 
Artur O. Lopes, Rafael O. Ruggiero. Large deviations and AubryMather measures supported in nonhyperbolic closed geodesics. Discrete & Continuous Dynamical Systems, 2011, 29 (3) : 11551174. doi: 10.3934/dcds.2011.29.1155 
[6] 
Yasuhiro Fujita, Katsushi Ohmori. Inequalities and the AubryMather theory of HamiltonJacobi equations. Communications on Pure & Applied Analysis, 2009, 8 (2) : 683688. doi: 10.3934/cpaa.2009.8.683 
[7] 
Diogo A. Gomes. Viscosity solution methods and the discrete AubryMather problem. Discrete & Continuous Dynamical Systems, 2005, 13 (1) : 103116. doi: 10.3934/dcds.2005.13.103 
[8] 
Siniša Slijepčević. The AubryMather theorem for driven generalized elastic chains. Discrete & Continuous Dynamical Systems, 2014, 34 (7) : 29833011. doi: 10.3934/dcds.2014.34.2983 
[9] 
Răzvan M. Tudoran. On the control of stability of periodic orbits of completely integrable systems. Journal of Geometric Mechanics, 2015, 7 (1) : 109124. doi: 10.3934/jgm.2015.7.109 
[10] 
Ernest Fontich, Pau Martín. Arnold diffusion in perturbations of analytic integrable Hamiltonian systems. Discrete & Continuous Dynamical Systems, 2001, 7 (1) : 6184. doi: 10.3934/dcds.2001.7.61 
[11] 
François Blanchard, Wen Huang. Entropy sets, weakly mixing sets and entropy capacity. Discrete & Continuous Dynamical Systems, 2008, 20 (2) : 275311. doi: 10.3934/dcds.2008.20.275 
[12] 
Roberto Camassa. Characteristics and the initial value problem of a completely integrable shallow water equation. Discrete & Continuous Dynamical Systems  B, 2003, 3 (1) : 115139. doi: 10.3934/dcdsb.2003.3.115 
[13] 
Lidong Wang, Hui Wang, Guifeng Huang. Minimal sets and $\omega$chaos in expansive systems with weak specification property. Discrete & Continuous Dynamical Systems, 2015, 35 (3) : 12311238. doi: 10.3934/dcds.2015.35.1231 
[14] 
Jianjun Paul Tian. Finitetime perturbations of dynamical systems and applications to tumor therapy. Discrete & Continuous Dynamical Systems  B, 2009, 12 (2) : 469479. doi: 10.3934/dcdsb.2009.12.469 
[15] 
Hassan Najafi Alishah, João Lopes Dias. Realization of tangent perturbations in discrete and continuous time conservative systems. Discrete & Continuous Dynamical Systems, 2014, 34 (12) : 53595374. doi: 10.3934/dcds.2014.34.5359 
[16] 
Jean René Chazottes, F. Durand. Local rates of Poincaré recurrence for rotations and weak mixing. Discrete & Continuous Dynamical Systems, 2005, 12 (1) : 175183. doi: 10.3934/dcds.2005.12.175 
[17] 
Oliver Knill. Singular continuous spectrum and quantitative rates of weak mixing. Discrete & Continuous Dynamical Systems, 1998, 4 (1) : 3342. doi: 10.3934/dcds.1998.4.33 
[18] 
Ethan M. Ackelsberg. Rigidity, weak mixing, and recurrence in abelian groups. Discrete & Continuous Dynamical Systems, 2021 doi: 10.3934/dcds.2021168 
[19] 
Jingang Zhao, Chi Zhang. Finitehorizon optimal control of discretetime linear systems with completely unknown dynamics using Qlearning. Journal of Industrial & Management Optimization, 2021, 17 (3) : 14711483. doi: 10.3934/jimo.2020030 
[20] 
P. Adda, J. L. Dimi, A. Iggidir, J. C. Kamgang, G. Sallet, J. J. Tewa. General models of hostparasite systems. Global analysis. Discrete & Continuous Dynamical Systems  B, 2007, 8 (1) : 117. doi: 10.3934/dcdsb.2007.8.1 
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]