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AIMS joins the mathematics community world wide in congratulating Professor Alessio Figalli on being awarded the Fields Medal 2018. Professor Figallihas made important contributions to AIMS journals and conferences. Heserved as the Managing Editor of Discrete and Continuous Dynamical Systemsfrom 2012 to 2016 and delivered a plenary lecture at the 11th AIMS conference (2016) in Orlando, USA. Details can be found at

Congratulations, Alessio!

DCDS, series A includes peer-reviewed original papers and invited expository papers on the theory and methods of analysis, differential equations and dynamical systems. This journal is committed to recording important new 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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Note: “Most Cited” is by Cross-Ref , and “Most Downloaded” is based on available data in the new website.

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Existence and uniqueness of very weak solution of the MHD type system
Yong Zeng
2020, 40(10) : 5617-5638 doi: 10.3934/dcds.2020240 +[Abstract](207) +[HTML](70) +[PDF](407.58KB)
Review of local and global existence results for stochastic pdes with Lévy noise
Justin Cyr, Phuong Nguyen, Sisi Tang and Roger Temam
2020, 40(10) : 5639-5710 doi: 10.3934/dcds.2020241 +[Abstract](78) +[HTML](33) +[PDF](922.2KB)
On the Yudovich's type solutions for the 2D Boussinesq system with thermal diffusivity
Marius Paicu and Ning Zhu
2020, 40(10) : 5711-5728 doi: 10.3934/dcds.2020242 +[Abstract](86) +[HTML](24) +[PDF](412.68KB)
A gradient flow approach of propagation of chaos
Samir Salem
2020, 40(10) : 5729-5754 doi: 10.3934/dcds.2020243 +[Abstract](86) +[HTML](30) +[PDF](517.03KB)
A simple proof of the Adams type inequalities in $ {\mathbb R}^{2m} $
Van Hoang Nguyen
2020, 40(10) : 5755-5764 doi: 10.3934/dcds.2020244 +[Abstract](67) +[HTML](33) +[PDF](319.65KB)
On the effects of firing memory in the dynamics of conjunctive networks
Eric Goles, Pedro Montealegre and Martín Ríos-Wilson
2020, 40(10) : 5765-5793 doi: 10.3934/dcds.2020245 +[Abstract](93) +[HTML](33) +[PDF](697.12KB)
Entropies of commuting transformations on Hilbert spaces
Zhiming Li and Yujun Zhu
2020, 40(10) : 5795-5814 doi: 10.3934/dcds.2020246 +[Abstract](81) +[HTML](25) +[PDF](427.19KB)
Evolution of dispersal in advective homogeneous environments
Li Ma and De Tang
2020, 40(10) : 5815-5830 doi: 10.3934/dcds.2020247 +[Abstract](81) +[HTML](28) +[PDF](316.0KB)
Existence of positive solutions of Schrödinger equations with vanishing potentials
Eduard Toon and Pedro Ubilla
2020, 40(10) : 5831-5843 doi: 10.3934/dcds.2020248 +[Abstract](101) +[HTML](18) +[PDF](330.67KB)
Analysis of a spatial memory model with nonlocal maturation delay and hostile boundary condition
Qi An, Chuncheng Wang and Hao Wang
2020, 40(10) : 5845-5868 doi: 10.3934/dcds.2020249 +[Abstract](109) +[HTML](31) +[PDF](4683.93KB)
Extended symmetry groups of multidimensional subshifts with hierarchical structure
Álvaro Bustos
2020, 40(10) : 5869-5895 doi: 10.3934/dcds.2020250 +[Abstract](118) +[HTML](32) +[PDF](925.6KB)
Continuous orbit equivalence of topological Markov shifts and KMS states on Cuntz–Krieger algebras
Kengo Matsumoto
2020, 40(10) : 5897-5909 doi: 10.3934/dcds.2020251 +[Abstract](93) +[HTML](20) +[PDF](360.25KB)
A degenerate KAM theorem for partial differential equations with periodic boundary conditions
Meina Gao and Jianjun Liu
2020, 40(10) : 5911-5928 doi: 10.3934/dcds.2020252 +[Abstract](62) +[HTML](22) +[PDF](388.36KB)
The two-component $ \mu $-Camassa–Holm system with peaked solutions
Yingying Li, Ying Fu and Changzheng Qu
2020, 40(10) : 5929-5954 doi: 10.3934/dcds.2020253 +[Abstract](97) +[HTML](31) +[PDF](598.66KB)
Gradient regularity for a singular parabolic equation in non-divergence form
Amal Attouchi and Eero Ruosteenoja
2020, 40(10) : 5955-5972 doi: 10.3934/dcds.2020254 +[Abstract](103) +[HTML](20) +[PDF](368.8KB)
Filtering the $ L^2- $critical focusing Schrödinger equation
Ruoci Sun
2020, 40(10) : 5973-5990 doi: 10.3934/dcds.2020255 +[Abstract](111) +[HTML](29) +[PDF](419.24KB)
Asymptotic behavior of global solutions to a class of heat equations with gradient nonlinearity
Caihong Chang, Qiangchang Ju and Zhengce Zhang
2020, 40(10) : 5991-6014 doi: 10.3934/dcds.2020256 +[Abstract](207) +[HTML](37) +[PDF](423.8KB)
Nonuniformly hyperbolic systems arising from coupling of chaotic and gradient-like systems
Matteo Tanzi and Lai-Sang Young
2020, 40(10) : 6015-6041 doi: 10.3934/dcds.2020257 +[Abstract](78) +[HTML](26) +[PDF](913.98KB)
No-shadowing for singular hyperbolic sets with a singularity
Xiao Wen and Lan Wen
2020, 40(10) : 6043-6059 doi: 10.3934/dcds.2020258 +[Abstract](89) +[HTML](19) +[PDF](341.76KB)
Integrability of moduli and regularity of denjoy counterexamples
Sang-hyun Kim and Thomas Koberda
2020, 40(10) : 6061-6088 doi: 10.3934/dcds.2020259 +[Abstract](89) +[HTML](27) +[PDF](449.9KB)
Rigidity of random group actions
Woochul Jung, Keonhee Lee, Carlos Morales and Jumi Oh
2020doi: 10.3934/dcds.2020130 +[Abstract](545) +[HTML](259) +[PDF](292.41KB)
Generic Birkhoff spectra
Zoltán Buczolich, Balázs Maga and Ryo Moore
2020doi: 10.3934/dcds.2020131 +[Abstract](423) +[HTML](229) +[PDF](484.2KB)
Maximal equicontinuous generic factors and weak model sets
Gerhard Keller
2020doi: 10.3934/dcds.2020132 +[Abstract](328) +[HTML](219) +[PDF](449.9KB)
The secant map applied to a real polynomial with multiple roots
Antonio Garijo and Xavier Jarque
2020doi: 10.3934/dcds.2020133 +[Abstract](344) +[HTML](221) +[PDF](492.96KB)
On the measure of KAM tori in two degrees of freedom
Luca Biasco and Luigi Chierchia
2020doi: 10.3934/dcds.2020134 +[Abstract](397) +[HTML](229) +[PDF](394.63KB)
Gaussian iterative algorithm and integrated automorphism equation for random means
Justyna Jarczyk and Witold Jarczyk
2020doi: 10.3934/dcds.2020135 +[Abstract](337) +[HTML](222) +[PDF](293.27KB)
Entire and ancient solutions of a supercritical semilinear heat equation
Peter Poláčik and Pavol Quittner
2020doi: 10.3934/dcds.2020136 +[Abstract](399) +[HTML](211) +[PDF](417.52KB)
Time-fractional equations with reaction terms: Fundamental solutions and asymptotics
Serena Dipierro, Benedetta Pellacci, Enrico Valdinoci and Gianmaria Verzini
2020doi: 10.3934/dcds.2020137 +[Abstract](480) +[HTML](233) +[PDF](373.7KB)
Hamiltonian elliptic systems in dimension two with arbitrary and double exponential growth conditions
João Marcos do Ó, Bruno Ribeiro and Bernhard Ruf
2020doi: 10.3934/dcds.2020138 +[Abstract](624) +[HTML](217) +[PDF](1397.84KB)
Computer assisted proofs of two-dimensional attracting invariant tori for ODEs
Maciej J. Capiński, Emmanuel Fleurantin and J. D. Mireles James
2020doi: 10.3934/dcds.2020162 +[Abstract](347) +[HTML](205) +[PDF](3490.25KB)
On the regularity of the Green current for semi-extremal endomorphisms of $ \mathbb{P}^2 $
Christophe Dupont and Axel Rogue
2020doi: 10.3934/dcds.2020163 +[Abstract](238) +[HTML](164) +[PDF](359.72KB)
On globally hypoelliptic abelian actions and their existence on homogeneous spaces
Danijela Damjanovic, James Tanis and Zhenqi Jenny Wang
2020doi: 10.3934/dcds.2020164 +[Abstract](255) +[HTML](172) +[PDF](534.48KB)
Euler integral and perihelion librations
Gabriella Pinzari
2020doi: 10.3934/dcds.2020165 +[Abstract](319) +[HTML](181) +[PDF](750.63KB)
A general mechanism of instability in Hamiltonian systems: Skipping along a normally hyperbolic invariant manifold
Marian Gidea, Rafael de la Llave and Tere M. Seara
2020doi: 10.3934/dcds.2020166 +[Abstract](434) +[HTML](169) +[PDF](358.85KB)
Mean equicontinuity, complexity and applications
Jie Li, Xiangdong Ye and Tao Yu
2020doi: 10.3934/dcds.2020167 +[Abstract](348) +[HTML](187) +[PDF](426.7KB)
A posteriori error estimates for self-similar solutions to the Euler equations
Alberto Bressan and Wen Shen
2020doi: 10.3934/dcds.2020168 +[Abstract](329) +[HTML](174) +[PDF](620.02KB)
Time dependent center manifold in PDEs
Hongyu Cheng and Rafael de la Llave
2020doi: 10.3934/dcds.2020213 +[Abstract](172) +[HTML](98) +[PDF](451.89KB)
Interval homeomorphic solutions of a functional equation of nonautonomous iterations
Xiao Tang, Yingying Zeng and Weinian Zhang
2020doi: 10.3934/dcds.2020214 +[Abstract](158) +[HTML](95) +[PDF](405.2KB)
Solitary-wave solutions of Benjamin-Ono and other systems for internal waves. I. approximations
Jerry L. Bona, Angel Durán and Dimitrios Mitsotakis
2020doi: 10.3934/dcds.2020215 +[Abstract](297) +[HTML](98) +[PDF](556.04KB)
Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction
Youshan Tao and Michael Winkler
2020doi: 10.3934/dcds.2020216 +[Abstract](181) +[HTML](96) +[PDF](373.71KB)
Uniqueness and exponential mixing for the measure of maximal entropy for piecewise hyperbolic maps
Mark F. Demers
2020doi: 10.3934/dcds.2020217 +[Abstract](186) +[HTML](82) +[PDF](702.9KB)
Minimal collision arcs asymptotic to central configurations
Vivina Barutello, Gian Marco Canneori and Susanna Terracini
2020doi: 10.3934/dcds.2020218 +[Abstract](198) +[HTML](93) +[PDF](523.35KB)
Mathematical analysis of a cloud resolving model including the ice microphysics
Yining Cao, Chuck Jia, Roger Temam and Joseph Tribbia
2020doi: 10.3934/dcds.2020219 +[Abstract](247) +[HTML](108) +[PDF](771.22KB)
Automatic sequences are orthogonal to aperiodic multiplicative functions
Mariusz Lemańczyk and Clemens Müllner
2020doi: 10.3934/dcds.2020260 +[Abstract](7) +[HTML](4) +[PDF](721.93KB)
Finding polynomial roots by dynamical systems – A case study
Sergey Shemyakov, Roman Chernov, Dzmitry Rumiantsau, Dierk Schleicher, Simon Schmitt and Anton Shemyakov
2020doi: 10.3934/dcds.2020261 +[Abstract](9) +[HTML](5) +[PDF](1181.27KB)
The Mandelbrot set is the shadow of a Julia set
François Berteloot and Tien-Cuong Dinh
2020doi: 10.3934/dcds.2020262 +[Abstract](8) +[HTML](5) +[PDF](457.84KB)
Stuart-type polar vortices on a rotating sphere
Adrian Constantin, Darren G. Crowdy, Vikas S. Krishnamurthy and Miles H. Wheeler
2020doi: 10.3934/dcds.2020263 +[Abstract](13) +[HTML](4) +[PDF](1625.53KB)
A brief and personal history of stochastic partial differential equations
Lorenzo Zambotti
2020doi: 10.3934/dcds.2020264 +[Abstract](8) +[HTML](4) +[PDF](442.35KB)
Symmetry and nonexistence results for a fractional Choquard equation with weights
Anh Tuan Duong, Phuong Le and Nhu Thang Nguyen
2020doi: 10.3934/dcds.2020265 +[Abstract](61) +[HTML](17) +[PDF](363.6KB)
The unique measure of maximal entropy for a compact rank one locally CAT(0) space
Russell Ricks
2020doi: 10.3934/dcds.2020266 +[Abstract](34) +[HTML](18) +[PDF](364.46KB)
Mean Li-Yorke chaotic set along polynomial sequence with full Hausdorff dimension for $ \beta $-transformation
Yuanfen Xiao
2020doi: 10.3934/dcds.2020267 +[Abstract](51) +[HTML](16) +[PDF](371.99KB)
Monotonicity for fractional Laplacian systems in unbounded Lipschitz domains
Lingwei Ma and Zhenqiu Zhang
2020doi: 10.3934/dcds.2020268 +[Abstract](40) +[HTML](25) +[PDF](394.66KB)
Local rigidity of certain solvable group actions on tori
Qiao Liu
2020doi: 10.3934/dcds.2020269 +[Abstract](39) +[HTML](18) +[PDF](325.3KB)
Pullback attractor for a weakly damped wave equation with sup-cubic nonlinearity
Xinyu Mei, Yangmin Xiong and Chunyou Sun
2020doi: 10.3934/dcds.2020270 +[Abstract](43) +[HTML](20) +[PDF](479.26KB)
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](5278) +[PDF](382.7KB) Cited By(252)
Well-posedness and blow-up phenomena for the 2-component Camassa-Holm equation
Joachim Escher, Olaf Lechtenfeld and Zhaoyang Yin
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Global attractors for damped semilinear wave equations
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Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation
Xiaoyue Li and Xuerong Mao
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Remarks on regularities for the 3D MHD equations
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The problem Of blow-up in nonlinear parabolic equations
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Global stability for damped Timoshenko systems
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Dissipative solutions for the Camassa-Holm equation
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Positive solution for a nonlinear stationary Schrödinger-Poisson system in $R^3$
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Regularity and classification of solutions to static Hartree equations involving fractional Laplacians
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A nonlinear parabolic-hyperbolic system for contact inhibition and a degenerate parabolic fisher kpp equation
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Traveling wave solutions of a highly nonlinear shallow water equation
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Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model
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On the spectral theory of positive operators and PDE applications
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