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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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Isomorphism and bi-Lipschitz equivalence between the univoque sets
Kan Jiang, Lifeng Xi, Shengnan Xu and Jinjin Yang
2020, 40(11) : 6089-6114 doi: 10.3934/dcds.2020271 +[Abstract](220) +[HTML](59) +[PDF](459.02KB)
Weak solutions to the continuous coagulation model with collisional breakage
Prasanta Kumar Barik and Ankik Kumar Giri
2020, 40(11) : 6115-6133 doi: 10.3934/dcds.2020272 +[Abstract](166) +[HTML](58) +[PDF](346.23KB)
Multitransition solutions for a generalized Frenkel-Kontorova model
Wen-Long Li and Xiaojun Cui
2020, 40(11) : 6135-6158 doi: 10.3934/dcds.2020273 +[Abstract](159) +[HTML](44) +[PDF](410.55KB)
On the Bidomain equations driven by stochastic forces
Matthias Hieber, Oleksandr Misiats and Oleksandr Stanzhytskyi
2020, 40(11) : 6159-6177 doi: 10.3934/dcds.2020274 +[Abstract](150) +[HTML](59) +[PDF](514.06KB)
Gromov-Hausdorff distances for dynamical systems
Nhan-Phu Chung
2020, 40(11) : 6179-6200 doi: 10.3934/dcds.2020275 +[Abstract](421) +[HTML](106) +[PDF](433.64KB)
Invariant manifolds and foliations for random differential equations driven by colored noise
Jun Shen, Kening Lu and Bixiang Wang
2020, 40(11) : 6201-6246 doi: 10.3934/dcds.2020276 +[Abstract](124) +[HTML](46) +[PDF](535.69KB)
The focusing logarithmic Schrödinger equation: Analysis of breathers and nonlinear superposition
Guillaume Ferriere
2020, 40(11) : 6247-6274 doi: 10.3934/dcds.2020277 +[Abstract](128) +[HTML](42) +[PDF](535.97KB)
On Morawetz estimates with time-dependent weights for the Klein-Gordon equation
Jungkwon Kim, Hyeongjin Lee, Ihyeok Seo and Jihyeon Seok
2020, 40(11) : 6275-6288 doi: 10.3934/dcds.2020279 +[Abstract](111) +[HTML](41) +[PDF](407.18KB)
Global existence of strong solutions to a biological network formulation model in 2+1 dimensions
Xiangsheng Xu
2020, 40(11) : 6289-6307 doi: 10.3934/dcds.2020280 +[Abstract](101) +[HTML](43) +[PDF](395.72KB)
Matching for a family of infinite measure continued fraction transformations
Charlene Kalle, Niels Langeveld, Marta Maggioni and Sara Munday
2020, 40(11) : 6309-6330 doi: 10.3934/dcds.2020281 +[Abstract](101) +[HTML](45) +[PDF](1063.31KB)
Compactness of transfer operators and spectral representation of Ruelle zeta functions for super-continuous functions
Katsukuni Nakagawa
2020, 40(11) : 6331-6350 doi: 10.3934/dcds.2020282 +[Abstract](145) +[HTML](44) +[PDF](390.8KB)
Energy transfer model and large periodic boundary value problem for the quintic nonlinear Schrödinger equations
Hideo Takaoka
2020, 40(11) : 6351-6378 doi: 10.3934/dcds.2020283 +[Abstract](91) +[HTML](53) +[PDF](458.39KB)
Global existence and large time behavior for the chemotaxis–shallow water system in a bounded domain
Weike Wang and Yucheng Wang
2020, 40(11) : 6379-6409 doi: 10.3934/dcds.2020284 +[Abstract](113) +[HTML](41) +[PDF](397.6KB)
Identifying varying magnetic anomalies using geomagnetic monitoring
Youjun Deng, Hongyu Liu and Wing-Yan Tsui
2020, 40(11) : 6411-6440 doi: 10.3934/dcds.2020285 +[Abstract](98) +[HTML](42) +[PDF](431.5KB)
A unified approach for energy scattering for focusing nonlinear Schrödinger equations
Van Duong Dinh
2020, 40(11) : 6441-6471 doi: 10.3934/dcds.2020286 +[Abstract](122) +[HTML](58) +[PDF](493.59KB)
On the global well-posedness of the axisymmetric viscous Boussinesq system in critical Lebesgue spaces
Adalet Hanachi, Haroune Houamed and Mohamed Zerguine
2020, 40(11) : 6473-6506 doi: 10.3934/dcds.2020287 +[Abstract](105) +[HTML](38) +[PDF](499.52KB)
Low regularity of solutions to the Rotation-Camassa-Holm type equation with the Coriolis effect
Runzhang Xu and Yanbing Yang
2020, 40(11) : 6507-6527 doi: 10.3934/dcds.2020288 +[Abstract](118) +[HTML](43) +[PDF](353.46KB)
The large diffusion limit for the heat equation in the exterior of the unit ball with a dynamical boundary condition
Marek Fila, Kazuhiro Ishige, Tatsuki Kawakami and Johannes Lankeit
2020, 40(11) : 6529-6546 doi: 10.3934/dcds.2020289 +[Abstract](102) +[HTML](43) +[PDF](351.82KB)
Global dynamics of a general Lotka-Volterra competition-diffusion system in heterogeneous environments
Qian Guo, Xiaoqing He and Wei-Ming Ni
2020, 40(11) : 6547-6573 doi: 10.3934/dcds.2020290 +[Abstract](152) +[HTML](66) +[PDF](476.51KB)
Rigidity of random group actions
Woochul Jung, Keonhee Lee, Carlos Morales and Jumi Oh
2020doi: 10.3934/dcds.2020130 +[Abstract](682) +[HTML](306) +[PDF](292.41KB)
Generic Birkhoff spectra
Zoltán Buczolich, Balázs Maga and Ryo Moore
2020doi: 10.3934/dcds.2020131 +[Abstract](529) +[HTML](263) +[PDF](484.2KB)
Maximal equicontinuous generic factors and weak model sets
Gerhard Keller
2020doi: 10.3934/dcds.2020132 +[Abstract](425) +[HTML](250) +[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](427) +[HTML](257) +[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](501) +[HTML](266) +[PDF](394.63KB)
Gaussian iterative algorithm and integrated automorphism equation for random means
Justyna Jarczyk and Witold Jarczyk
2020doi: 10.3934/dcds.2020135 +[Abstract](425) +[HTML](248) +[PDF](293.27KB)
Entire and ancient solutions of a supercritical semilinear heat equation
Peter Poláčik and Pavol Quittner
2020doi: 10.3934/dcds.2020136 +[Abstract](505) +[HTML](242) +[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](577) +[HTML](269) +[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](727) +[HTML](248) +[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](445) +[HTML](256) +[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](319) +[HTML](194) +[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](331) +[HTML](208) +[PDF](534.48KB)
Euler integral and perihelion librations
Gabriella Pinzari
2020doi: 10.3934/dcds.2020165 +[Abstract](400) +[HTML](211) +[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](546) +[HTML](211) +[PDF](358.85KB)
Mean equicontinuity, complexity and applications
Jie Li, Xiangdong Ye and Tao Yu
2020doi: 10.3934/dcds.2020167 +[Abstract](458) +[HTML](224) +[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](427) +[HTML](210) +[PDF](620.02KB)
Time dependent center manifold in PDEs
Hongyu Cheng and Rafael de la Llave
2020doi: 10.3934/dcds.2020213 +[Abstract](258) +[HTML](139) +[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](239) +[HTML](134) +[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](412) +[HTML](139) +[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](293) +[HTML](136) +[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](262) +[HTML](121) +[PDF](702.9KB)
Minimal collision arcs asymptotic to central configurations
Vivina Barutello, Gian Marco Canneori and Susanna Terracini
2020doi: 10.3934/dcds.2020218 +[Abstract](288) +[HTML](128) +[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](350) +[HTML](147) +[PDF](771.22KB)
Automatic sequences are orthogonal to aperiodic multiplicative functions
Mariusz Lemańczyk and Clemens Müllner
2020doi: 10.3934/dcds.2020260 +[Abstract](146) +[HTML](52) +[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](129) +[HTML](62) +[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](111) +[HTML](54) +[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](159) +[HTML](58) +[PDF](1625.53KB)
A brief and personal history of stochastic partial differential equations
Lorenzo Zambotti
2020doi: 10.3934/dcds.2020264 +[Abstract](129) +[HTML](56) +[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](182) +[HTML](68) +[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](136) +[HTML](66) +[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](148) +[HTML](56) +[PDF](371.99KB)
Monotonicity for fractional Laplacian systems in unbounded Lipschitz domains
Lingwei Ma and Zhenqiu Zhang
2020doi: 10.3934/dcds.2020268 +[Abstract](138) +[HTML](68) +[PDF](394.66KB)
Local rigidity of certain solvable group actions on tori
Qiao Liu
2020doi: 10.3934/dcds.2020269 +[Abstract](136) +[HTML](61) +[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](159) +[HTML](59) +[PDF](479.26KB)
Maximal factors of order $ d $ of dynamical cubespaces
Jiahao Qiu and Jianjie Zhao
2020doi: 10.3934/dcds.2020278 +[Abstract](7) +[HTML](10) +[PDF](361.03KB)
Singular solutions of a Lane-Emden system
Craig Cowan and Abdolrahman Razani
2020doi: 10.3934/dcds.2020291 +[Abstract](64) +[HTML](44) +[PDF](492.3KB)
Uniform stability estimate for the Vlasov-Poisson-Boltzmann system
Hao Wang
2020doi: 10.3934/dcds.2020292 +[Abstract](59) +[HTML](27) +[PDF](371.02KB)
Asymptotic behavior of minimal solutions of $ -\Delta u = \lambda f(u) $ as $ \lambda\to-\infty $
Luca Battaglia, Francesca Gladiali and Massimo Grossi
2020doi: 10.3934/dcds.2020293 +[Abstract](49) +[HTML](21) +[PDF](411.09KB)
Local limit theorems for suspended semiflows
Jon Aaronson and Dalia Terhesiu
2020doi: 10.3934/dcds.2020294 +[Abstract](47) +[HTML](33) +[PDF](696.74KB)
How to identify a hyperbolic set as a blender
Stefanie Hittmeyer, Bernd Krauskopf, Hinke M. Osinga and Katsutoshi Shinohara
2020doi: 10.3934/dcds.2020295 +[Abstract](48) +[HTML](27) +[PDF](3606.1KB)
Function approximation via the subsampled Poincaré inequality
Yifan Chen and Thomas Y. Hou
2020doi: 10.3934/dcds.2020296 +[Abstract](58) +[HTML](34) +[PDF](574.91KB)
Strongly localized semiclassical states for nonlinear Dirac equations
Thomas Bartsch and Tian Xu
2020doi: 10.3934/dcds.2020297 +[Abstract](60) +[HTML](28) +[PDF](459.75KB)
Construction of a solitary wave solution of the nonlinear focusing schrödinger equation outside a strictly convex obstacle in the $ L^2 $-supercritical case
Oussama Landoulsi
2020doi: 10.3934/dcds.2020298 +[Abstract](0) +[HTML](0) +[PDF](577.9KB)
Large time behavior of exchange-driven growth
Emre Esentürk and Juan Velazquez
2020doi: 10.3934/dcds.2020299 +[Abstract](0) +[HTML](0) +[PDF](459.76KB)
Attainability property for a probabilistic target in wasserstein spaces
Giulia Cavagnari and Antonio Marigonda
2020doi: 10.3934/dcds.2020300 +[Abstract](0) +[HTML](0) +[PDF](644.37KB)
Asymptotic dynamics of a system of conservation laws from chemotaxis
Neng Zhu, Zhengrong Liu, Fang Wang and Kun Zhao
2020doi: 10.3934/dcds.2020301 +[Abstract](1) +[HTML](0) +[PDF](406.44KB)
Well-posedness of some non-linear stable driven SDEs
Noufel Frikha, Valentin Konakov and Stéphane Menozzi
2020doi: 10.3934/dcds.2020302 +[Abstract](0) +[HTML](0) +[PDF](672.72KB)
A generalization of the Babbage functional equation
Marc Homs-Dones
2020doi: 10.3934/dcds.2020303 +[Abstract](0) +[HTML](1) +[PDF](427.53KB)
Low Mach number limit for the compressible inertial Qian-Sheng model of liquid crystals: Convergence for classical solutions
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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](1) +[HTML](0) +[PDF](379.01KB)
$ N- $Laplacian problems with critical double exponential nonlinearities
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Pomeau-Manneville maps are global-local mixing
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Existence uniqueness and regularity theory for elliptic equations with complex-valued potentials
Tuoc Phan, Grozdena Todorova and Borislav Yordanov
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Solution of the 33rd Palis-Pugh problem for gradient-like diffeomorphisms of a two-dimensional sphere
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Long time behavior of the fractional Korteweg-de Vries equation with cubic nonlinearity
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Periodic solutions and Hyers-Ulam stability of atmospheric Ekman flows
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Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
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Well-posedness and blow-up phenomena for the 2-component Camassa-Holm 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 universality of the incompressible Euler equation on compact manifolds
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Ground state solutions of Nehari-Pohozaev type for Schrödinger-Poisson problems with general potentials
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