American Institute of Mathematical Sciences

Dongfeng Zhang, Junxiang Xu. On elliptic lower dimensional tori for Gevrey-smooth Hamiltonian systems under Rüssmann's non-degeneracy condition. Discrete and Continuous Dynamical Systems, 2006, 16 (3) : 635-655. doi: 10.3934/dcds.2006.16.635

Helmut Rüssmann. KAM iteration with nearly infinitely small steps in dynamical systems of polynomial character. Discrete and Continuous Dynamical Systems - S, 2010, 3 (4) : 683-718. doi: 10.3934/dcdss.2010.3.683

Pedro J. Torres, Zhibo Cheng, Jingli Ren. Non-degeneracy and uniqueness of periodic solutions for $2n$-order differential equations. Discrete and Continuous Dynamical Systems, 2013, 33 (5) : 2155-2168. doi: 10.3934/dcds.2013.33.2155

Lipeng Duan, Jun Yang. On the non-degeneracy of radial vortex solutions for a coupled Ginzburg-Landau system. Discrete and Continuous Dynamical Systems, 2021, 41 (10) : 4767-4790. doi: 10.3934/dcds.2021056

Robert Magnus, Olivier Moschetta. The non-linear Schrödinger equation with non-periodic potential: infinite-bump solutions and non-degeneracy. Communications on Pure and Applied Analysis, 2012, 11 (2) : 587-626. doi: 10.3934/cpaa.2012.11.587

Xiaocai Wang, Junxiang Xu, Dongfeng Zhang. A KAM theorem for the elliptic lower dimensional tori with one normal frequency in reversible systems. Discrete and Continuous Dynamical Systems, 2017, 37 (4) : 2141-2160. doi: 10.3934/dcds.2017092

Xiaocai Wang. Non-floquet invariant tori in reversible systems. Discrete and Continuous Dynamical Systems, 2018, 38 (7) : 3439-3457. doi: 10.3934/dcds.2018147

Xuemei Li, Zaijiu Shang. On the existence of invariant tori in non-conservative dynamical systems with degeneracy and finite differentiability. Discrete and Continuous Dynamical Systems, 2019, 39 (7) : 4225-4257. doi: 10.3934/dcds.2019171

Paul H. Rabinowitz. On a class of reversible elliptic systems. Networks and Heterogeneous Media, 2012, 7 (4) : 927-939. doi: 10.3934/nhm.2012.7.927

Mark Comerford, Todd Woodard. Orbit portraits in non-autonomous iteration. Discrete and Continuous Dynamical Systems - S, 2019, 12 (8) : 2253-2277. doi: 10.3934/dcdss.2019144

Fuzhong Cong, Yong Li. Invariant hyperbolic tori for Hamiltonian systems with degeneracy. Discrete and Continuous Dynamical Systems, 1997, 3 (3) : 371-382. doi: 10.3934/dcds.1997.3.371

Genni Fragnelli, Dimitri Mugnai. Singular parabolic equations with interior degeneracy and non smooth coefficients: The Neumann case. Discrete and Continuous Dynamical Systems - S, 2020, 13 (5) : 1495-1511. doi: 10.3934/dcdss.2020084

JinHyon Kim, HyonHui Ju, WiJong An. Inheritance of $ {\mathscr F}- $chaos and $ {\mathscr F}- $sensitivities under an iteration for non-autonomous discrete systems. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022053

Peter Giesl. Necessary condition for the basin of attraction of a periodic orbit in non-smooth periodic systems. Discrete and Continuous Dynamical Systems, 2007, 18 (2&3) : 355-373. doi: 10.3934/dcds.2007.18.355

Marina Gonchenko, Sergey Gonchenko, Klim Safonov. Reversible perturbations of conservative Hénon-like maps. Discrete and Continuous Dynamical Systems, 2021, 41 (4) : 1875-1895. doi: 10.3934/dcds.2020343

Marco Ghimenti, A. M. Micheletti. Non degeneracy for solutions of singularly perturbed nonlinear elliptic problems on symmetric Riemannian manifolds. Communications on Pure and Applied Analysis, 2013, 12 (2) : 679-693. doi: 10.3934/cpaa.2013.12.679

André Vanderbauwhede. Continuation and bifurcation of multi-symmetric solutions in reversible Hamiltonian systems. Discrete and Continuous Dynamical Systems, 2013, 33 (1) : 359-363. doi: 10.3934/dcds.2013.33.359

B. Coll, Chengzhi Li, Rafel Prohens. Quadratic perturbations of a class of quadratic reversible systems with two centers. Discrete and Continuous Dynamical Systems, 2009, 24 (3) : 699-729. doi: 10.3934/dcds.2009.24.699

Ricardo Miranda Martins. Formal equivalence between normal forms of reversible and hamiltonian dynamical systems. Communications on Pure and Applied Analysis, 2014, 13 (2) : 703-713. doi: 10.3934/cpaa.2014.13.703

Yuncheng You. Asymptotic dynamics of reversible cubic autocatalytic reaction-diffusion systems. Communications on Pure and Applied Analysis, 2011, 10 (5) : 1415-1445. doi: 10.3934/cpaa.2011.10.1415