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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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Maciej Capiński, Núria Fagella, Michał Misiurewicz, Weixiao Shen, Benjamin Weiss and Krzysztof Ciepliński
2020, 40(12) : ⅰ-ⅱ doi: 10.3934/dcds.2020327 +[Abstract](324) +[HTML](105) +[PDF](74.53KB)
Local limit theorems for suspended semiflows
Jon Aaronson and Dalia Terhesiu
2020, 40(12) : 6575-6609 doi: 10.3934/dcds.2020294 +[Abstract](296) +[HTML](73) +[PDF](714.45KB)
The Mandelbrot set is the shadow of a Julia set
François Berteloot and Tien-Cuong Dinh
2020, 40(12) : 6611-6633 doi: 10.3934/dcds.2020262 +[Abstract](375) +[HTML](99) +[PDF](423.41KB)
On the measure of KAM tori in two degrees of freedom
Luca Biasco and Luigi Chierchia
2020, 40(12) : 6635-6648 doi: 10.3934/dcds.2020134 +[Abstract](741) +[HTML](302) +[PDF](404.79KB)
Generic Birkhoff spectra
Zoltán Buczolich, Balázs Maga and Ryo Moore
2020, 40(12) : 6649-6679 doi: 10.3934/dcds.2020131 +[Abstract](774) +[HTML](356) +[PDF](493.71KB)
Computer assisted proofs of two-dimensional attracting invariant tori for ODEs
Maciej J. Capiński, Emmanuel Fleurantin and J. D. Mireles James
2020, 40(12) : 6681-6707 doi: 10.3934/dcds.2020162 +[Abstract](740) +[HTML](347) +[PDF](3490.25KB)
Time dependent center manifold in PDEs
Hongyu Cheng and Rafael de la Llave
2020, 40(12) : 6709-6745 doi: 10.3934/dcds.2020213 +[Abstract](503) +[HTML](237) +[PDF](475.68KB)
On globally hypoelliptic abelian actions and their existence on homogeneous spaces
Danijela Damjanovic, James Tanis and Zhenqi Jenny Wang
2020, 40(12) : 6747-6766 doi: 10.3934/dcds.2020164 +[Abstract](541) +[HTML](296) +[PDF](576.23KB)
On the regularity of the Green current for semi-extremal endomorphisms of $ \mathbb{P}^2 $
Christophe Dupont and Axel Rogue
2020, 40(12) : 6767-6781 doi: 10.3934/dcds.2020163 +[Abstract](509) +[HTML](275) +[PDF](376.35KB)
The secant map applied to a real polynomial with multiple roots
Antonio Garijo and Xavier Jarque
2020, 40(12) : 6783-6794 doi: 10.3934/dcds.2020133 +[Abstract](628) +[HTML](342) +[PDF](509.6KB)
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
2020, 40(12) : 6795-6813 doi: 10.3934/dcds.2020166 +[Abstract](807) +[HTML](302) +[PDF](376.13KB)
How to identify a hyperbolic set as a blender
Stefanie Hittmeyer, Bernd Krauskopf, Hinke M. Osinga and Katsutoshi Shinohara
2020, 40(12) : 6815-6836 doi: 10.3934/dcds.2020295 +[Abstract](301) +[HTML](131) +[PDF](3623.24KB)
Gaussian iterative algorithm and integrated automorphism equation for random means
Justyna Jarczyk and Witold Jarczyk
2020, 40(12) : 6837-6844 doi: 10.3934/dcds.2020135 +[Abstract](648) +[HTML](280) +[PDF](310.32KB)
Rigidity of random group actions
Woochul Jung, Keonhee Lee, Carlos Morales and Jumi Oh
2020, 40(12) : 6845-6854 doi: 10.3934/dcds.2020130 +[Abstract](908) +[HTML](397) +[PDF](316.07KB)
Maximal equicontinuous generic factors and weak model sets
Gerhard Keller
2020, 40(12) : 6855-6875 doi: 10.3934/dcds.2020132 +[Abstract](641) +[HTML](336) +[PDF](466.14KB)
Automatic sequences are orthogonal to aperiodic multiplicative functions
Mariusz Lemańczyk and Clemens Müllner
2020, 40(12) : 6877-6918 doi: 10.3934/dcds.2020260 +[Abstract](357) +[HTML](147) +[PDF](593.34KB)
Euler integral and perihelion librations
Gabriella Pinzari
2020, 40(12) : 6919-6943 doi: 10.3934/dcds.2020165 +[Abstract](617) +[HTML](293) +[PDF](760.42KB)
Finding polynomial roots by dynamical systems – A case study
Sergey Shemyakov, Roman Chernov, Dzmitry Rumiantsau, Dierk Schleicher, Simon Schmitt and Anton Shemyakov
2020, 40(12) : 6945-6965 doi: 10.3934/dcds.2020261 +[Abstract](381) +[HTML](157) +[PDF](1150.32KB)
Interval homeomorphic solutions of a functional equation of nonautonomous iterations
Xiao Tang, Yingying Zeng and Weinian Zhang
2020, 40(12) : 6967-6984 doi: 10.3934/dcds.2020214 +[Abstract](475) +[HTML](222) +[PDF](422.1KB)
Entire and ancient solutions of a supercritical semilinear heat equation
Peter Poláčik and Pavol Quittner
2020doi: 10.3934/dcds.2020136 +[Abstract](741) +[HTML](333) +[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](820) +[HTML](361) +[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](926) +[HTML](337) +[PDF](1397.84KB)
Mean equicontinuity, complexity and applications
Jie Li, Xiangdong Ye and Tao Yu
2020doi: 10.3934/dcds.2020167 +[Abstract](671) +[HTML](309) +[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](630) +[HTML](297) +[PDF](620.02KB)
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](662) +[HTML](245) +[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](475) +[HTML](217) +[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](445) +[HTML](202) +[PDF](702.9KB)
Minimal collision arcs asymptotic to central configurations
Vivina Barutello, Gian Marco Canneori and Susanna Terracini
2020doi: 10.3934/dcds.2020218 +[Abstract](464) +[HTML](206) +[PDF](523.35KB)
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Yining Cao, Chuck Jia, Roger Temam and Joseph Tribbia
2020doi: 10.3934/dcds.2020219 +[Abstract](531) +[HTML](232) +[PDF](771.22KB)
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](368) +[HTML](151) +[PDF](1625.53KB)
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Lorenzo Zambotti
2020doi: 10.3934/dcds.2020264 +[Abstract](367) +[HTML](167) +[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](457) +[HTML](159) +[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](301) +[HTML](156) +[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](323) +[HTML](139) +[PDF](371.99KB)
Monotonicity for fractional Laplacian systems in unbounded Lipschitz domains
Lingwei Ma and Zhenqiu Zhang
2020doi: 10.3934/dcds.2020268 +[Abstract](307) +[HTML](169) +[PDF](394.66KB)
Local rigidity of certain solvable group actions on tori
Qiao Liu
2020doi: 10.3934/dcds.2020269 +[Abstract](307) +[HTML](149) +[PDF](325.3KB)
Pullback attractor for a weakly damped wave equation with sup-cubic nonlinearity
Xinyu Mei, Yangmin Xiong and Chunyou Sun
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Maximal factors of order $ d $ of dynamical cubespaces
Jiahao Qiu and Jianjie Zhao
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Singular solutions of a Lane-Emden system
Craig Cowan and Abdolrahman Razani
2020doi: 10.3934/dcds.2020291 +[Abstract](269) +[HTML](131) +[PDF](492.3KB)
Uniform stability estimate for the Vlasov-Poisson-Boltzmann system
Hao Wang
2020doi: 10.3934/dcds.2020292 +[Abstract](309) +[HTML](122) +[PDF](371.02KB)
Asymptotic behavior of minimal solutions of $ -\Delta u = \lambda f(u) $ as $ \lambda\to-\infty $
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2020doi: 10.3934/dcds.2020293 +[Abstract](220) +[HTML](108) +[PDF](411.09KB)
Function approximation via the subsampled Poincaré inequality
Yifan Chen and Thomas Y. Hou
2020doi: 10.3934/dcds.2020296 +[Abstract](230) +[HTML](175) +[PDF](574.91KB)
Strongly localized semiclassical states for nonlinear Dirac equations
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2020doi: 10.3934/dcds.2020298 +[Abstract](222) +[HTML](103) +[PDF](577.9KB)
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2020doi: 10.3934/dcds.2020299 +[Abstract](200) +[HTML](101) +[PDF](459.76KB)
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2020doi: 10.3934/dcds.2020301 +[Abstract](204) +[HTML](102) +[PDF](406.44KB)
Well-posedness of some non-linear stable driven SDEs
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A generalization of the Babbage functional equation
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2020doi: 10.3934/dcds.2020303 +[Abstract](227) +[HTML](115) +[PDF](427.53KB)
Low Mach number limit for the compressible inertial Qian-Sheng model of liquid crystals: Convergence for classical solutions
Yi-Long Luo and Yangjun Ma
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Geometric singular perturbation analysis of Degasperis-Procesi equation with distributed delay
Feifei Cheng and Ji Li
2020doi: 10.3934/dcds.2020305 +[Abstract](253) +[HTML](103) +[PDF](379.01KB)
$ N- $Laplacian problems with critical double exponential nonlinearities
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2020doi: 10.3934/dcds.2020306 +[Abstract](175) +[HTML](96) +[PDF](386.87KB)
Recoding Lie algebraic subshifts
Ville Salo and Ilkka Törmä
2020doi: 10.3934/dcds.2020307 +[Abstract](241) +[HTML](108) +[PDF](361.8KB)
Properties of the minimizers for a constrained minimization problem arising in Kirchhoff equation
Helin Guo and Huan-Song Zhou
2020doi: 10.3934/dcds.2020308 +[Abstract](208) +[HTML](97) +[PDF](470.54KB)
Pomeau-Manneville maps are global-local mixing
Claudio Bonanno and Marco Lenci
2020doi: 10.3934/dcds.2020309 +[Abstract](240) +[HTML](109) +[PDF](380.22KB)
Existence uniqueness and regularity theory for elliptic equations with complex-valued potentials
Tuoc Phan, Grozdena Todorova and Borislav Yordanov
2020doi: 10.3934/dcds.2020310 +[Abstract](277) +[HTML](125) +[PDF](432.97KB)
Solution of the 33rd Palis-Pugh problem for gradient-like diffeomorphisms of a two-dimensional sphere
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2020doi: 10.3934/dcds.2020311 +[Abstract](206) +[HTML](120) +[PDF](24076.94KB)
Long time behavior of the fractional Korteweg-de Vries equation with cubic nonlinearity
Jean-Claude Saut and Yuexun Wang
2020doi: 10.3934/dcds.2020312 +[Abstract](250) +[HTML](108) +[PDF](359.14KB)
Periodic solutions and Hyers-Ulam stability of atmospheric Ekman flows
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2020doi: 10.3934/dcds.2020313 +[Abstract](200) +[HTML](113) +[PDF](391.87KB)
Multiple ergodic averages for tempered functions
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2020doi: 10.3934/dcds.2020314 +[Abstract](186) +[HTML](110) +[PDF](491.36KB)
Asymptotic stability in a chemotaxis-competition system with indirect signal production
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2020doi: 10.3934/dcds.2020315 +[Abstract](167) +[HTML](92) +[PDF](390.91KB)
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Andrew Comech and Scipio Cuccagna
2020doi: 10.3934/dcds.2020316 +[Abstract](165) +[HTML](90) +[PDF](609.62KB)
On entropy of $ \Phi $-irregular and $ \Phi $-level sets in maps with the shadowing property
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2020doi: 10.3934/dcds.2020317 +[Abstract](181) +[HTML](88) +[PDF](451.5KB)
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Entropy production in random billiards
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Gromov-Hausdorff stability for group actions
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Sharp regularity for degenerate obstacle type problems: A geometric approach
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Failure of scattering to solitary waves for long-range nonlinear Schrödinger equations
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Julián Fernández Bonder, Analía Silva and Juan F. Spedaletti
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Radially Symmetric Stationary Wave for Two-dimensional Burgers Equation
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2020doi: 10.3934/dcds.2020357 +[Abstract](1) +[HTML](0) +[PDF](392.96KB)
Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
Jie Shen and Xiaofeng Yang
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Well-posedness and blow-up phenomena for the 2-component Camassa-Holm equation
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2013, 33(5) : 2105-2137 doi: 10.3934/dcds.2013.33.2105 +[Abstract](4242) +[PDF](418.8KB) Cited By(198)
Global attractors for damped semilinear wave equations
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Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation
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