
Previous Article
Uniform inertial sets for damped wave equations
 DCDS Home
 This Issue

Next Article
Pursuitevasion games with state constraints: dynamic programming and discretetime approximations
Transition tori near an ellipticfixed point
1.  Departmento de Matematicas, UAMIztapalapa, C. P. 09340, A. P. 55534 Mexico DF, Mexico 
In this situation, the homoclinic map $\Lambda$ is a smooth and symplectic diffeomorphism of open subsets of the central manifold of $\mathbf a$.
Moreover, if an invariant circle intersects the domain of definition of $\Lambda$ and its image intersects other circle, there are orbits that wander from one circle to the other. This phenomenon is similar to the Arnold diffusion.
The Melnikov Method gives sufficient conditions for the existence of homoclinic maps, and non identity homoclinic maps in a perturbation of a Hamiltonian system.
[1] 
Leilei Wei, Yinnian He. A fully discrete local discontinuous Galerkin method with the generalized numerical flux to solve the tempered fractional reactiondiffusion equation. Discrete & Continuous Dynamical Systems  B, 2020 doi: 10.3934/dcdsb.2020319 
[2] 
Tian Ma, Shouhong Wang. Topological phase transition III: Solar surface eruptions and sunspots. Discrete & Continuous Dynamical Systems  B, 2020 doi: 10.3934/dcdsb.2020350 
[3] 
Antoine Benoit. Weak wellposedness of hyperbolic boundary value problems in a strip: when instabilities do not reflect the geometry. Communications on Pure & Applied Analysis, 2020, 19 (12) : 54755486. doi: 10.3934/cpaa.2020248 
[4] 
Chao Xing, Jiaojiao Pan, Hong Luo. Stability and dynamic transition of a toxinproducing phytoplanktonzooplankton model with additional food. Communications on Pure & Applied Analysis, , () : . doi: 10.3934/cpaa.2020275 
[5] 
Mehdi Bastani, Davod Khojasteh Salkuyeh. On the GSOR iteration method for image restoration. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 2743. doi: 10.3934/naco.2020013 
[6] 
Hong Niu, Zhijiang Feng, Qijin Xiao, Yajun Zhang. A PID control method based on optimal control strategy. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 117126. doi: 10.3934/naco.2020019 
[7] 
Weiwei Liu, Jinliang Wang, Yuming Chen. Threshold dynamics of a delayed nonlocal reactiondiffusion cholera model. Discrete & Continuous Dynamical Systems  B, 2020 doi: 10.3934/dcdsb.2020316 
[8] 
Abdelghafour Atlas, Mostafa Bendahmane, Fahd Karami, Driss Meskine, Omar Oubbih. A nonlinear fractional reactiondiffusion system applied to image denoising and decomposition. Discrete & Continuous Dynamical Systems  B, 2020 doi: 10.3934/dcdsb.2020321 
[9] 
PierreEtienne Druet. A theory of generalised solutions for ideal gas mixtures with MaxwellStefan diffusion. Discrete & Continuous Dynamical Systems  S, 2020 doi: 10.3934/dcdss.2020458 
[10] 
LiBin Liu, Ying Liang, Jian Zhang, Xiaobing Bao. A robust adaptive grid method for singularly perturbed BurgerHuxley equations. Electronic Research Archive, 2020, 28 (4) : 14391457. doi: 10.3934/era.2020076 
[11] 
Zexuan Liu, Zhiyuan Sun, Jerry Zhijian Yang. A numerical study of superconvergence of the discontinuous Galerkin method by patch reconstruction. Electronic Research Archive, 2020, 28 (4) : 14871501. doi: 10.3934/era.2020078 
[12] 
Yuxia Guo, Shaolong Peng. A direct method of moving planes for fully nonlinear nonlocal operators and applications. Discrete & Continuous Dynamical Systems  S, 2020 doi: 10.3934/dcdss.2020462 
[13] 
Noah Stevenson, Ian Tice. A truncated real interpolation method and characterizations of screened Sobolev spaces. Communications on Pure & Applied Analysis, 2020, 19 (12) : 55095566. doi: 10.3934/cpaa.2020250 
[14] 
Yue Feng, Yujie Liu, Ruishu Wang, Shangyou Zhang. A conforming discontinuous Galerkin finite element method on rectangular partitions. Electronic Research Archive, , () : . doi: 10.3934/era.2020120 
[15] 
S. Sadeghi, H. Jafari, S. Nemati. Solving fractional Advectiondiffusion equation using Genocchi operational matrix based on AtanganaBaleanu derivative. Discrete & Continuous Dynamical Systems  S, 2020 doi: 10.3934/dcdss.2020435 
[16] 
H. M. Srivastava, H. I. AbdelGawad, Khaled Mohammed Saad. Oscillatory states and patterns formation in a twocell cubic autocatalytic reactiondiffusion model subjected to the Dirichlet conditions. Discrete & Continuous Dynamical Systems  S, 2020 doi: 10.3934/dcdss.2020433 
[17] 
Lin Shi, Xuemin Wang, Dingshi Li. Limiting behavior of nonautonomous stochastic reactiondiffusion equations with colored noise on unbounded thin domains. Communications on Pure & Applied Analysis, 2020, 19 (12) : 53675386. doi: 10.3934/cpaa.2020242 
[18] 
HaiFeng Huo, ShiKe Hu, Hong Xiang. Traveling wave solution for a diffusion SEIR epidemic model with selfprotection and treatment. Electronic Research Archive, , () : . doi: 10.3934/era.2020118 
[19] 
Marion Darbas, Jérémy Heleine, Stephanie Lohrengel. Numerical resolution by the quasireversibility method of a data completion problem for Maxwell's equations. Inverse Problems & Imaging, 2020, 14 (6) : 11071133. doi: 10.3934/ipi.2020056 
[20] 
Gang Bao, Mingming Zhang, Bin Hu, Peijun Li. An adaptive finite element DtN method for the threedimensional acoustic scattering problem. Discrete & Continuous Dynamical Systems  B, 2020 doi: 10.3934/dcdsb.2020351 
2019 Impact Factor: 1.338
Tools
Metrics
Other articles
by authors
[Back to Top]