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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  http://aimsciences.org/conferences/2016/2016_speakers.html

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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Preface
Maciej Capiński, Núria Fagella, Michał Misiurewicz, Weixiao Shen, Benjamin Weiss and Krzysztof Ciepliński
2020, 40(12) : ⅰ-ⅱ doi: 10.3934/dcds.2020327 +[Abstract](246) +[HTML](81) +[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](229) +[HTML](71) +[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](307) +[HTML](96) +[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](675) +[HTML](301) +[PDF](404.79KB)
Generic Birkhoff spectra
Zoltán Buczolich, Balázs Maga and Ryo Moore
2020, 40(12) : 6649-6679 doi: 10.3934/dcds.2020131 +[Abstract](709) +[HTML](333) +[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](667) +[HTML](325) +[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](441) +[HTML](208) +[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](479) +[HTML](275) +[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](460) +[HTML](255) +[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](583) +[HTML](319) +[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](746) +[HTML](281) +[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](230) +[HTML](101) +[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](591) +[HTML](278) +[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](854) +[HTML](377) +[PDF](316.07KB)
Maximal equicontinuous generic factors and weak model sets
Gerhard Keller
2020, 40(12) : 6855-6875 doi: 10.3934/dcds.2020132 +[Abstract](578) +[HTML](314) +[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](304) +[HTML](122) +[PDF](593.34KB)
Euler integral and perihelion librations
Gabriella Pinzari
2020, 40(12) : 6919-6943 doi: 10.3934/dcds.2020165 +[Abstract](565) +[HTML](269) +[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](317) +[HTML](132) +[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](416) +[HTML](193) +[PDF](422.1KB)
Entire and ancient solutions of a supercritical semilinear heat equation
Peter Poláčik and Pavol Quittner
2020doi: 10.3934/dcds.2020136 +[Abstract](676) +[HTML](308) +[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](760) +[HTML](338) +[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](875) +[HTML](311) +[PDF](1397.84KB)
Mean equicontinuity, complexity and applications
Jie Li, Xiangdong Ye and Tao Yu
2020doi: 10.3934/dcds.2020167 +[Abstract](618) +[HTML](285) +[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](581) +[HTML](268) +[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](599) +[HTML](207) +[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](428) +[HTML](192) +[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](392) +[HTML](178) +[PDF](702.9KB)
Minimal collision arcs asymptotic to central configurations
Vivina Barutello, Gian Marco Canneori and Susanna Terracini
2020doi: 10.3934/dcds.2020218 +[Abstract](426) +[HTML](181) +[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](479) +[HTML](203) +[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](302) +[HTML](127) +[PDF](1625.53KB)
A brief and personal history of stochastic partial differential equations
Lorenzo Zambotti
2020doi: 10.3934/dcds.2020264 +[Abstract](281) +[HTML](137) +[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](379) +[HTML](133) +[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](260) +[HTML](133) +[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](283) +[HTML](114) +[PDF](371.99KB)
Monotonicity for fractional Laplacian systems in unbounded Lipschitz domains
Lingwei Ma and Zhenqiu Zhang
2020doi: 10.3934/dcds.2020268 +[Abstract](266) +[HTML](137) +[PDF](394.66KB)
Local rigidity of certain solvable group actions on tori
Qiao Liu
2020doi: 10.3934/dcds.2020269 +[Abstract](260) +[HTML](119) +[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](292) +[HTML](119) +[PDF](479.26KB)
Maximal factors of order $ d $ of dynamical cubespaces
Jiahao Qiu and Jianjie Zhao
2020doi: 10.3934/dcds.2020278 +[Abstract](166) +[HTML](77) +[PDF](361.03KB)
Singular solutions of a Lane-Emden system
Craig Cowan and Abdolrahman Razani
2020doi: 10.3934/dcds.2020291 +[Abstract](214) +[HTML](103) +[PDF](492.3KB)
Uniform stability estimate for the Vlasov-Poisson-Boltzmann system
Hao Wang
2020doi: 10.3934/dcds.2020292 +[Abstract](200) +[HTML](96) +[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](160) +[HTML](81) +[PDF](411.09KB)
Function approximation via the subsampled Poincaré inequality
Yifan Chen and Thomas Y. Hou
2020doi: 10.3934/dcds.2020296 +[Abstract](179) +[HTML](132) +[PDF](574.91KB)
Strongly localized semiclassical states for nonlinear Dirac equations
Thomas Bartsch and Tian Xu
2020doi: 10.3934/dcds.2020297 +[Abstract](206) +[HTML](93) +[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](169) +[HTML](71) +[PDF](577.9KB)
Large time behavior of exchange-driven growth
Emre Esentürk and Juan Velazquez
2020doi: 10.3934/dcds.2020299 +[Abstract](147) +[HTML](70) +[PDF](459.76KB)
Attainability property for a probabilistic target in wasserstein spaces
Giulia Cavagnari and Antonio Marigonda
2020doi: 10.3934/dcds.2020300 +[Abstract](143) +[HTML](69) +[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](151) +[HTML](70) +[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](211) +[HTML](74) +[PDF](672.72KB)
A generalization of the Babbage functional equation
Marc Homs-Dones
2020doi: 10.3934/dcds.2020303 +[Abstract](178) +[HTML](85) +[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
2020doi: 10.3934/dcds.2020304 +[Abstract](174) +[HTML](75) +[PDF](532.57KB)
Geometric singular perturbation analysis of Degasperis-Procesi equation with distributed delay
Feifei Cheng and Ji Li
2020doi: 10.3934/dcds.2020305 +[Abstract](179) +[HTML](72) +[PDF](379.01KB)
$ N- $Laplacian problems with critical double exponential nonlinearities
Shengbing Deng, Tingxi Hu and Chun-Lei Tang
2020doi: 10.3934/dcds.2020306 +[Abstract](130) +[HTML](67) +[PDF](386.87KB)
Recoding Lie algebraic subshifts
Ville Salo and Ilkka Törmä
2020doi: 10.3934/dcds.2020307 +[Abstract](195) +[HTML](76) +[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](158) +[HTML](71) +[PDF](470.54KB)
Pomeau-Manneville maps are global-local mixing
Claudio Bonanno and Marco Lenci
2020doi: 10.3934/dcds.2020309 +[Abstract](182) +[HTML](81) +[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](215) +[HTML](84) +[PDF](432.97KB)
Solution of the 33rd Palis-Pugh problem for gradient-like diffeomorphisms of a two-dimensional sphere
Elena Nozdrinova and Olga Pochinka
2020doi: 10.3934/dcds.2020311 +[Abstract](146) +[HTML](82) +[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](191) +[HTML](82) +[PDF](359.14KB)
Periodic solutions and Hyers-Ulam stability of atmospheric Ekman flows
Yi Guan, Michal Fečkan and Jinrong Wang
2020doi: 10.3934/dcds.2020313 +[Abstract](151) +[HTML](82) +[PDF](391.87KB)
Multiple ergodic averages for tempered functions
Andreas Koutsogiannis
2020doi: 10.3934/dcds.2020314 +[Abstract](141) +[HTML](79) +[PDF](491.36KB)
Asymptotic stability in a chemotaxis-competition system with indirect signal production
Pan Zheng
2020doi: 10.3934/dcds.2020315 +[Abstract](121) +[HTML](56) +[PDF](390.91KB)
On asymptotic stability of ground states of some systems of nonlinear Schrödinger equations
Andrew Comech and Scipio Cuccagna
2020doi: 10.3934/dcds.2020316 +[Abstract](122) +[HTML](63) +[PDF](609.62KB)
On entropy of $ \Phi $-irregular and $ \Phi $-level sets in maps with the shadowing property
Magdalena Foryś-Krawiec, Jiří Kupka, Piotr Oprocha and Xueting Tian
2020doi: 10.3934/dcds.2020317 +[Abstract](126) +[HTML](62) +[PDF](451.5KB)
Blow-up and bounded solutions for a semilinear parabolic problem in a saturable medium
Juliana Fernandes and Liliane Maia
2020doi: 10.3934/dcds.2020318 +[Abstract](121) +[HTML](64) +[PDF](393.23KB)
Entropy production in random billiards
Timothy Chumley and Renato Feres
2020doi: 10.3934/dcds.2020319 +[Abstract](105) +[HTML](54) +[PDF](889.91KB)
Gromov-Hausdorff stability for group actions
Meihua Dong, Keonhee Lee and Carlos Morales
2020doi: 10.3934/dcds.2020320 +[Abstract](103) +[HTML](48) +[PDF](257.96KB)
Sharp regularity for degenerate obstacle type problems: A geometric approach
João Vitor da Silva and Hernán Vivas
2020doi: 10.3934/dcds.2020321 +[Abstract](88) +[HTML](36) +[PDF](505.09KB)
Global large solutions and optimal time-decay estimates to the Korteweg system
Xiaoping Zhai and Yongsheng Li
2020doi: 10.3934/dcds.2020322 +[Abstract](102) +[HTML](40) +[PDF](437.18KB)
A sharp scattering threshold level for mass-subcritical nonlinear Schrödinger system
Masaru Hamano and Satoshi Masaki
2020doi: 10.3934/dcds.2020323 +[Abstract](95) +[HTML](46) +[PDF](492.71KB)
Mean-square random invariant manifolds for stochastic differential equations
Bixiang Wang
2020doi: 10.3934/dcds.2020324 +[Abstract](99) +[HTML](39) +[PDF](360.68KB)
Global graph of metric entropy on expanding Blaschke products
Yunping Jiang
2020doi: 10.3934/dcds.2020325 +[Abstract](78) +[HTML](37) +[PDF](325.86KB)
Existence of nodal solutions for the sublinear Moore-Nehari differential equation
Ryuji Kajikiya
2020doi: 10.3934/dcds.2020326 +[Abstract](81) +[HTML](39) +[PDF](380.59KB)
Failure of scattering to solitary waves for long-range nonlinear Schrödinger equations
Jason Murphy and Kenji Nakanishi
2020doi: 10.3934/dcds.2020328 +[Abstract](76) +[HTML](29) +[PDF](361.49KB)
Averaging of Hamilton-Jacobi equations along divergence-free vector fields
Hitoshi Ishii and Taiga Kumagai
2020doi: 10.3934/dcds.2020329 +[Abstract](66) +[HTML](27) +[PDF](413.61KB)
Jordan decomposition and the recurrent set of flows of automorphisms
Víctor Ayala, Adriano Da Silva and Philippe Jouan
2020doi: 10.3934/dcds.2020330 +[Abstract](75) +[HTML](28) +[PDF](388.19KB)
A Liouville theorem of parabolic Monge-AmpÈre equations in half-space
Ziwei Zhou, Jiguang Bao and Bo Wang
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Well-posedness for the three dimensional stochastic planetary geostrophic equations of large-scale ocean circulation
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Classification of nonnegative solutions to an equation involving the Laplacian of arbitrary order
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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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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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The problem Of blow-up in nonlinear parabolic equations
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Vacuum states for compressible flow
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Partial regularity of the dynamic system modeling the flow of liquid crystals
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Some questions looking for answers in dynamical systems
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The problem Of blow-up in nonlinear parabolic equations
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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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Uniqueness of positive radial solutions of a semilinear elliptic equation in an annulus
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Differentiability of the Hartman--Grobman linearization
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On the universality of the incompressible Euler equation on compact manifolds
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