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Discrete and Continuous Dynamical Systems (DCDS) publishes peer-reviewed original and expository papers on the theory, methods and applications of analysis, differential equations and dynamical systems. The journal is committed to recording important new methods and results in its field and maintains the highest standards of innovation and quality. To be published in this journal, an original paper must be correct, new, nontrivial and of interest to a substantial number of readers.

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Analytic linearization of a generalization of the semi-standard map: Radius of convergence and Brjuno sum
Claire Chavaudret and Stefano Marmi
2022, 42(7) : 3077-3101 doi: 10.3934/dcds.2022009 +[Abstract](207) +[HTML](100) +[PDF](2520.4KB)
Orbital stability for the mass-critical and supercritical pseudo-relativistic nonlinear Schrödinger equation
Younghun Hong and Sangdon Jin
2022, 42(7) : 3103-3118 doi: 10.3934/dcds.2022010 +[Abstract](266) +[HTML](100) +[PDF](382.44KB)
Singular solutions of Toda system in high dimensions
Linlin Dou
2022, 42(7) : 3119-3142 doi: 10.3934/dcds.2022011 +[Abstract](231) +[HTML](125) +[PDF](374.1KB)
Vortex collapses for the Euler and Quasi-Geostrophic models
Ludovic Godard-Cadillac
2022, 42(7) : 3143-3168 doi: 10.3934/dcds.2022012 +[Abstract](248) +[HTML](94) +[PDF](427.01KB)
A KAM theorem for quasi-periodic non-twist mappings and its application
Zhichao Ma and Junxiang Xu
2022, 42(7) : 3169-3185 doi: 10.3934/dcds.2022013 +[Abstract](249) +[HTML](103) +[PDF](340.92KB)
Introducing sub-Riemannian and sub-Finsler billiards
Lucas Dahinden and Álvaro del Pino
2022, 42(7) : 3187-3232 doi: 10.3934/dcds.2022014 +[Abstract](191) +[HTML](88) +[PDF](1375.68KB)
Regularity of almost-minimizers of Hölder-coefficient surface energies
David A. Simmons
2022, 42(7) : 3233-3299 doi: 10.3934/dcds.2022015 +[Abstract](187) +[HTML](80) +[PDF](634.45KB)
Existence of positive solutions for a class of fractional Choquard equation in exterior domain
César E. Torres Ledesma
2022, 42(7) : 3301-3328 doi: 10.3934/dcds.2022016 +[Abstract](230) +[HTML](83) +[PDF](391.9KB)
Multiplicity results for elliptic problems involving nonlocal integrodifferential operators without Ambrosetti-Rabinowitz condition
Lauren M. M. Bonaldo, Elard J. Hurtado and Olímpio H. Miyagaki
2022, 42(7) : 3329-3353 doi: 10.3934/dcds.2022017 +[Abstract](188) +[HTML](75) +[PDF](442.56KB)
Linear stability of exact solutions for the generalized Kaup-Boussinesq equation and their dynamical evolutions
Ruizhi Gong, Yuren Shi and Deng-Shan Wang
2022, 42(7) : 3355-3378 doi: 10.3934/dcds.2022018 +[Abstract](190) +[HTML](160) +[PDF](769.7KB)
Polynomial ergodic averages for certain countable ring actions
Andrew Best and Andreu Ferré Moragues
2022, 42(7) : 3379-3413 doi: 10.3934/dcds.2022019 +[Abstract](165) +[HTML](73) +[PDF](511.71KB)
SRB measures of singular hyperbolic attractors
Dominic Veconi
2022, 42(7) : 3415-3430 doi: 10.3934/dcds.2022020 +[Abstract](188) +[HTML](78) +[PDF](326.68KB)
Asymptotics of ODE's flow on the torus through a singleton condition and a perturbation result. Applications
Marc Briane and Loïc Hervé
2022, 42(7) : 3431-3463 doi: 10.3934/dcds.2022021 +[Abstract](164) +[HTML](75) +[PDF](466.77KB)
A combinatorial approach to Rauzy-type dynamics II: The labelling method and a second proof of the KZB classification theorem
Quentin De Mourgues
2022, 42(7) : 3465-3538 doi: 10.3934/dcds.2022022 +[Abstract](131) +[HTML](68) +[PDF](1079.83KB)
On a class of singularly perturbed elliptic systems with asymptotic phase segregation
Farid Bozorgnia, Martin Burger and Morteza Fotouhi
2022, 42(7) : 3539-3556 doi: 10.3934/dcds.2022023 +[Abstract](158) +[HTML](67) +[PDF](1496.34KB)
On decomposition of ambient surfaces admitting $ A $-diffeomorphisms with non-trivial attractors and repellers
Vyacheslav Grines and Dmitrii Mints
2022, 42(7) : 3557-3568 doi: 10.3934/dcds.2022024 +[Abstract](135) +[HTML](69) +[PDF](841.03KB)
Particle approximation of one-dimensional Mean-Field-Games with local interactions
Marco Di Francesco, Serikbolsyn Duisembay, Diogo Aguiar Gomes and Ricardo Ribeiro
2022, 42(7) : 3569-3591 doi: 10.3934/dcds.2022025 +[Abstract](149) +[HTML](63) +[PDF](609.67KB)
On information gain, Kullback-Leibler divergence, entropy production and the involution kernel
Artur O. Lopes and Jairo K. Mengue
2022, 42(7) : 3593-3627 doi: 10.3934/dcds.2022026 +[Abstract](112) +[HTML](61) +[PDF](506.57KB)
Mach limits in analytic spaces on exterior domains
Juhi Jang, Igor Kukavica and Linfeng Li
2022doi: 10.3934/dcds.2022027 +[Abstract](126) +[HTML](52) +[PDF](409.48KB)
On the long-time behavior for a damped Navier-Stokes-Bardina model
Oscar Jarrín and Manuel Fernando Cortez
2022doi: 10.3934/dcds.2022028 +[Abstract](131) +[HTML](49) +[PDF](511.81KB)
The sandpile identity element on an ellipse
Andrew Melchionna
2022doi: 10.3934/dcds.2022029 +[Abstract](167) +[HTML](48) +[PDF](1045.39KB)
Global solutions of semilinear parabolic equations with drift term on Riemannian manifolds
Fabio Punzo
2022doi: 10.3934/dcds.2022030 +[Abstract](123) +[HTML](47) +[PDF](323.12KB)
Bogdanov-Takens bifurcation with $ Z_2 $ symmetry and spatiotemporal dynamics in diffusive Rosenzweig-MacArthur model involving nonlocal prey competition
Xun Cao, Xianyong Chen and Weihua Jiang
2022doi: 10.3934/dcds.2022031 +[Abstract](170) +[HTML](144) +[PDF](1362.65KB)
Maximal regularity for time-stepping schemes arising from convolution quadrature of non-local in time equations
Carlos Lizama and Marina Murillo-Arcila
2022doi: 10.3934/dcds.2022032 +[Abstract](117) +[HTML](65) +[PDF](425.5KB)
Dynamically learning the parameters of a chaotic system using partial observations
Elizabeth Carlson, Joshua Hudson, Adam Larios, Vincent R. Martinez, Eunice Ng and Jared P. Whitehead
2022doi: 10.3934/dcds.2022033 +[Abstract](127) +[HTML](52) +[PDF](3815.51KB)
A game theoretical approximation for a parabolic/elliptic system with different operators
Alfredo Miranda and Julio D. Rossi
2022doi: 10.3934/dcds.2022034 +[Abstract](113) +[HTML](54) +[PDF](449.12KB)
Enhanced existence time of solutions to evolution equations of Whitham type
Mats Ehrnström and Yuexun Wang
2022doi: 10.3934/dcds.2022035 +[Abstract](88) +[HTML](34) +[PDF](421.87KB)
Singular solutions of some elliptic equations involving mixed absorption-reaction
Marie-Françoise Bidaut-Véron, Marta Garcia-Huidobro and Laurent Véron
2022doi: 10.3934/dcds.2022036 +[Abstract](152) +[HTML](36) +[PDF](1017.97KB)
A Moser theorem for multiscale mappings
Xuefeng Zhao and Yong Li
2022doi: 10.3934/dcds.2022037 +[Abstract](100) +[HTML](40) +[PDF](335.7KB)
Gibbs measures for hyperbolic attractors defined by densities
David Parmenter and Mark Pollicott
2022doi: 10.3934/dcds.2022038 +[Abstract](157) +[HTML](45) +[PDF](425.63KB)
Examples of finite time blow up in mass dissipative reaction-diffusion systems with superquadratic growth
Michel Pierre and Didier Schmitt
2022doi: 10.3934/dcds.2022039 +[Abstract](118) +[HTML](47) +[PDF](401.97KB)
Radon measure-valued solutions of unsteady filtration equations
Maria Michaela Porzio, Flavia Smarrazzo and Alberto Tesei
2022doi: 10.3934/dcds.2022040 +[Abstract](95) +[HTML](38) +[PDF](459.36KB)
Renormalized solutions for stochastic $ p $-Laplace equations with $ L^1 $-initial data: The case of multiplicative noise
Niklas Sapountzoglou and Aleksandra Zimmermann
2022doi: 10.3934/dcds.2022041 +[Abstract](99) +[HTML](54) +[PDF](375.96KB)
A shrinking target theorem for ergodic transformations of the unit interval
Shrey Sanadhya
2022doi: 10.3934/dcds.2022042 +[Abstract](113) +[HTML](36) +[PDF](302.47KB)
Unfolding globally resonant homoclinic tangencies
Sishu Shankar Muni, Robert I. McLachlan and David J. W. Simpson
2022doi: 10.3934/dcds.2022043 +[Abstract](101) +[HTML](38) +[PDF](758.56KB)
Local behavior of solutions to a fractional equation with isolated singularity and critical Serrin exponent
Juncheng Wei and Ke Wu
2022doi: 10.3934/dcds.2022044 +[Abstract](108) +[HTML](37) +[PDF](364.44KB)
A fixed point theorem for twist maps
Zhihong Xia and Peizheng Yu
2022doi: 10.3934/dcds.2022045 +[Abstract](119) +[HTML](40) +[PDF](316.2KB)
Concentrated solutions for a critical elliptic equation
Lipeng Duan and Shuying Tian
2022doi: 10.3934/dcds.2022046 +[Abstract](98) +[HTML](42) +[PDF](498.01KB)
Boundedness and stabilization of a three-dimensional parabolic-elliptic Keller-Segel-Stokes system
Pengmei Zhang and Jiashan Zheng
2022doi: 10.3934/dcds.2022047 +[Abstract](125) +[HTML](65) +[PDF](638.22KB)
Normal form coordinates for the Benjamin-Ono equation having expansions in terms of pseudo-differential operators
Thomas Kappeler and Riccardo Montalto
2022doi: 10.3934/dcds.2022048 +[Abstract](99) +[HTML](37) +[PDF](898.95KB)
The Neumann problem for a class of mixed complex Hessian equations
Chuanqiang Chen, Li Chen, Xinqun Mei and Ni Xiang
2022doi: 10.3934/dcds.2022049 +[Abstract](100) +[HTML](39) +[PDF](347.41KB)
Mean dimension theory in symbolic dynamics for finitely generated amenable groups
Yunping Wang, Ercai Chen and Xiaoyao Zhou
2022doi: 10.3934/dcds.2022050 +[Abstract](100) +[HTML](40) +[PDF](361.87KB)
Achievable connectivities of Fatou components for a family of singular perturbations
Jordi Canela, Xavier Jarque and Dan Paraschiv
2022doi: 10.3934/dcds.2022051 +[Abstract](86) +[HTML](31) +[PDF](1546.74KB)
An upper bound of the measure-theoretical entropy
Yuntao Zang
2022doi: 10.3934/dcds.2022052 +[Abstract](89) +[HTML](32) +[PDF](676.72KB)
Instability results for the logarithmic Sobolev inequality and its application to related inequalities
Daesung Kim
2022doi: 10.3934/dcds.2022053 +[Abstract](100) +[HTML](33) +[PDF](478.44KB)
The topology of Bott integrable fluids
Robert Cardona
2022doi: 10.3934/dcds.2022054 +[Abstract](110) +[HTML](36) +[PDF](630.18KB)
Stability of a class of action functionals depending on convex functions
Luigi Ambrosio and Camillo Brena
2022doi: 10.3934/dcds.2022055 +[Abstract](87) +[HTML](30) +[PDF](317.18KB)
Elliptic systems with nonlinear diffusion and a convection term
Lucio Boccardo and Luigi Orsina
2022doi: 10.3934/dcds.2022056 +[Abstract](88) +[HTML](31) +[PDF](353.88KB)
Limit theorems for higher rank actions on Heisenberg nilmanifolds
Minsung Kim
2022doi: 10.3934/dcds.2022057 +[Abstract](92) +[HTML](25) +[PDF](568.68KB)
Global existence and blow up for systems of nonlinear wave equations related to the weak null condition
Kunio Hidano and Kazuyoshi Yokoyama
2022doi: 10.3934/dcds.2022058 +[Abstract](88) +[HTML](33) +[PDF](433.14KB)
Critical gauged Schrödinger equations in $ \mathbb{R}^2 $ with vanishing potentials
Liejun Shen, Marco Squassina and Minbo Yang
2022doi: 10.3934/dcds.2022059 +[Abstract](96) +[HTML](25) +[PDF](449.24KB)
Long-time asymptotics for the modified complex short pulse equation
Mingming Chen, Xianguo Geng and Kedong Wang
2022doi: 10.3934/dcds.2022060 +[Abstract](134) +[HTML](43) +[PDF](481.3KB)
Comparison principles for nonlocal Hamilton-Jacobi equations
Gonzalo Dávila
2022doi: 10.3934/dcds.2022061 +[Abstract](100) +[HTML](23) +[PDF](328.35KB)
Global existence of weak solutions for the 3D axisymmetric chemotaxis-Navier-Stokes equations with nonlinear diffusion
Xiaoyu Chen, Jijie Zhao and Qian Zhang
2022doi: 10.3934/dcds.2022062 +[Abstract](117) +[HTML](33) +[PDF](436.84KB)
Global well-posedness of 2D incompressible Magnetohydrodynamic equations with horizontal dissipation
Xiaoxiao Suo and Quansen Jiu
2022doi: 10.3934/dcds.2022063 +[Abstract](34) +[HTML](12) +[PDF](362.48KB)
Invariant tori for the derivative nonlinear Schrödinger equation with nonlinear term depending on spatial variable
Zhaowei Lou, Jianguo Si and Shimin Wang
2022doi: 10.3934/dcds.2022064 +[Abstract](40) +[HTML](9) +[PDF](519.65KB)
Bismut formula for intrinsic/Lions derivatives of distribution dependent SDEs with singular coefficients
Xing Huang, Yulin Song and Feng-Yu Wang
2022doi: 10.3934/dcds.2022065 +[Abstract](30) +[HTML](9) +[PDF](369.31KB)
Global well-posedness of the Cauchy problem for the Jordan–Moore–Gibson–Thompson equation with arbitrarily large higher-order Sobolev norms
Belkacem Said-Houari
2022doi: 10.3934/dcds.2022066 +[Abstract](45) +[HTML](14) +[PDF](344.54KB)
Multiple ergodic averages for variable polynomials
Andreas Koutsogiannis
2022doi: 10.3934/dcds.2022067 +[Abstract](39) +[HTML](15) +[PDF](499.13KB)
Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
Jie Shen and Xiaofeng Yang
2010, 28(4) : 1669-1691 doi: 10.3934/dcds.2010.28.1669 +[Abstract](10147) +[PDF](382.7KB) Cited By(319)
Variational methods for non-local operators of elliptic type
Raffaella Servadei and Enrico Valdinoci
2013, 33(5) : 2105-2137 doi: 10.3934/dcds.2013.33.2105 +[Abstract](6700) +[PDF](418.8KB) Cited By(292)
Global well-posedness of the viscous Boussinesq equations
Thomas Y. Hou and Congming Li
2005, 12(1) : 1-12 doi: 10.3934/dcds.2005.12.1 +[Abstract](5069) +[PDF](203.5KB) Cited By(209)
Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation
Xiaoyue Li and Xuerong Mao
2009, 24(2) : 523-545 doi: 10.3934/dcds.2009.24.523 +[Abstract](8798) +[PDF](262.8KB) Cited By(202)
Well-posedness and blow-up phenomena for the 2-component Camassa-Holm equation
Joachim Escher, Olaf Lechtenfeld and Zhaoyang Yin
2007, 19(3) : 493-513 doi: 10.3934/dcds.2007.19.493 +[Abstract](6404) +[PDF](233.8KB) Cited By(202)
Global attractors for damped semilinear wave equations
John M. Ball
2004, 10(1&2) : 31-52 doi: 10.3934/dcds.2004.10.31 +[Abstract](7873) +[PDF](246.2KB) Cited By(198)
Partial regularity of the dynamic system modeling the flow of liquid crystals
Fanghua Lin and Chun Liu
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The problem Of blow-up in nonlinear parabolic equations
Victor A. Galaktionov and Juan-Luis Vázquez
2002, 8(2) : 399-433 doi: 10.3934/dcds.2002.8.399 +[Abstract](7466) +[PDF](369.4KB) Cited By(169)
Remarks on regularities for the 3D MHD equations
Yong Zhou
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Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model
Linda J. S. Allen, B. M. Bolker, Yuan Lou and A. L. Nevai
2008, 21(1) : 1-20 doi: 10.3934/dcds.2008.21.1 +[Abstract](9490) +[PDF](401.1KB) Cited By(155)
The problem Of blow-up in nonlinear parabolic equations
Victor A. Galaktionov and Juan-Luis Vázquez
2002, 8(2) : 399-433 doi: 10.3934/dcds.2002.8.399 +[Abstract](7466) +[PDF](369.4KB) PDF Downloads(2305)
Some questions looking for answers in dynamical systems
Carles Simó
2018, 38(12) : 6215-6239 doi: 10.3934/dcds.2018267 +[Abstract](6356) +[HTML](372) +[PDF](531.03KB) PDF Downloads(2020)
The vorticity equation on a rotating sphere and the shallow fluid approximation
Vikas S. Krishnamurthy
2019, 39(11) : 6261-6276 doi: 10.3934/dcds.2019273 +[Abstract](2481) +[HTML](168) +[PDF](370.02KB) PDF Downloads(1854)
Conditional measures and conditional expectation; Rohlin's Disintegration Theorem
David Simmons
2012, 32(7) : 2565-2582 doi: 10.3934/dcds.2012.32.2565 +[Abstract](4500) +[PDF](444.9KB) PDF Downloads(1610)
Differentiability of the Hartman--Grobman linearization
Misha Guysinsky, Boris Hasselblatt and Victoria Rayskin
2003, 9(4) : 979-984 doi: 10.3934/dcds.2003.9.979 +[Abstract](3239) +[PDF](131.0KB) PDF Downloads(1218)
Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
Jie Shen and Xiaofeng Yang
2010, 28(4) : 1669-1691 doi: 10.3934/dcds.2010.28.1669 +[Abstract](10147) +[PDF](382.7KB) PDF Downloads(1133)
Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model
Linda J. S. Allen, B. M. Bolker, Yuan Lou and A. L. Nevai
2008, 21(1) : 1-20 doi: 10.3934/dcds.2008.21.1 +[Abstract](9490) +[PDF](401.1KB) PDF Downloads(1027)
Understanding Thomas-Fermi-Like approximations: Averaging over oscillating occupied orbitals
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On the spectral theory of positive operators and PDE applications
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On Geometric Mechanics
Jean-Marie Souriau
2007, 19(3) : 595-607 doi: 10.3934/dcds.2007.19.595 +[Abstract](2904) +[PDF](183.4KB) PDF Downloads(872)

2020 Impact Factor: 1.392
5 Year Impact Factor: 1.610
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