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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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Boundary layer for 3D plane parallel channel flows of nonhomogeneous incompressible Navier-Stokes equations
Shijin Ding, Zhilin Lin and Dongjuan Niu
2020, 40(8) : 4579-4596 doi: 10.3934/dcds.2020193 +[Abstract](287) +[HTML](72) +[PDF](371.51KB)
Magnus-type integrator for non-autonomous SPDEs driven by multiplicative noise
Antoine Tambue and Jean Daniel Mukam
2020, 40(8) : 4597-4624 doi: 10.3934/dcds.2020194 +[Abstract](193) +[HTML](64) +[PDF](492.57KB)
Ruelle operator for continuous potentials and DLR-Gibbs measures
Leandro Cioletti, Artur O. Lopes and Manuel Stadlbauer
2020, 40(8) : 4625-4652 doi: 10.3934/dcds.2020195 +[Abstract](207) +[HTML](56) +[PDF](446.59KB)
Structure of accessibility classes
Jana Rodriguez Hertz and Carlos H. Vásquez
2020, 40(8) : 4653-4664 doi: 10.3934/dcds.2020196 +[Abstract](203) +[HTML](56) +[PDF](309.35KB)
Fluctuations of ergodic sums on periodic orbits under specification
Manfred Denker, Samuel Senti and Xuan Zhang
2020, 40(8) : 4665-4687 doi: 10.3934/dcds.2020197 +[Abstract](338) +[HTML](68) +[PDF](407.62KB)
Existence of periodic waves for a perturbed quintic BBM equation
Lina Guo and Yulin Zhao
2020, 40(8) : 4689-4703 doi: 10.3934/dcds.2020198 +[Abstract](115) +[HTML](54) +[PDF](254.25KB)
Representation formula for symmetrical symplectic capacity and applications
Rongrong Jin and Guangcun Lu
2020, 40(8) : 4705-4765 doi: 10.3934/dcds.2020199 +[Abstract](97) +[HTML](50) +[PDF](670.45KB)
Mean dimension of shifts of finite type and of generalized inverse limits
Kazuhiro Kawamura
2020, 40(8) : 4767-4775 doi: 10.3934/dcds.2020200 +[Abstract](107) +[HTML](46) +[PDF](302.54KB)
Exponential upper bounds on the spectral gaps and homogeneous spectrum for the non-critical extended Harper's model
Xu Xu and Xin Zhao
2020, 40(8) : 4777-4800 doi: 10.3934/dcds.2020201 +[Abstract](116) +[HTML](57) +[PDF](534.62KB)
Asymptotic behavior for a Schrödinger equation with nonlinear subcritical dissipation
Thierry Cazenave and Zheng Han
2020, 40(8) : 4801-4819 doi: 10.3934/dcds.2020202 +[Abstract](131) +[HTML](46) +[PDF](393.49KB)
Classification to the positive radial solutions with weighted biharmonic equation
Xia Huang and Liping Wang
2020, 40(8) : 4821-4837 doi: 10.3934/dcds.2020203 +[Abstract](136) +[HTML](53) +[PDF](402.71KB)
Critically finite random maps of an interval
Jason Atnip and Mariusz Urbański
2020, 40(8) : 4839-4906 doi: 10.3934/dcds.2020204 +[Abstract](105) +[HTML](54) +[PDF](630.73KB)
Representation formulas of solutions and bifurcation sheets to a nonlocal Allen-Cahn equation
Tatsuki Mori, Kousuke Kuto, Tohru Tsujikawa and Shoji Yotsutani
2020, 40(8) : 4907-4925 doi: 10.3934/dcds.2020205 +[Abstract](114) +[HTML](59) +[PDF](815.51KB)
A structure-preserving scheme for the Allen–Cahn equation with a dynamic boundary condition
Makoto Okumura and Daisuke Furihata
2020, 40(8) : 4927-4960 doi: 10.3934/dcds.2020206 +[Abstract](162) +[HTML](47) +[PDF](699.91KB)
Positivity, monotonicity, and convexity for convolution operators
Christopher Goodrich and Carlos Lizama
2020, 40(8) : 4961-4983 doi: 10.3934/dcds.2020207 +[Abstract](127) +[HTML](68) +[PDF](388.15KB)
Lifespan of solutions to the Strauss type wave system on asymptotically flat space-times
Wei Dai, Daoyuan Fang and Chengbo Wang
2020, 40(8) : 4985-4999 doi: 10.3934/dcds.2020208 +[Abstract](85) +[HTML](49) +[PDF](439.15KB)
Blowup results and concentration in focusing Schrödinger-Hartree equation
Yingying Xie, Jian Su and Liquan Mei
2020, 40(8) : 5001-5017 doi: 10.3934/dcds.2020209 +[Abstract](124) +[HTML](45) +[PDF](417.11KB)
$ L^p $ Neumann problems in homogenization of general elliptic operators
Li Wang, Qiang Xu and Shulin Zhou
2020, 40(8) : 5019-5045 doi: 10.3934/dcds.2020210 +[Abstract](138) +[HTML](43) +[PDF](463.0KB)
Asymptotic behavior of sign-changing radial solutions of a semilinear elliptic equation in $ \mathbb{R}^2 $ when exponent approaches $ +\infty $
Weiwei Ao and Chao Liu
2020, 40(8) : 5047-5077 doi: 10.3934/dcds.2020211 +[Abstract](179) +[HTML](43) +[PDF](476.57KB)
On a discrete self-organized-criticality finite time result
Umberto Mosco and Maria Agostina Vivaldi
2020, 40(8) : 5079-5103 doi: 10.3934/dcds.2020212 +[Abstract](94) +[HTML](47) +[PDF](386.69KB)
Rigidity of random group actions
Woochul Jung, Keonhee Lee, Carlos Morales and Jumi Oh
2020doi: 10.3934/dcds.2020130 +[Abstract](363) +[HTML](192) +[PDF](292.41KB)
Generic Birkhoff spectra
Zoltán Buczolich, Balázs Maga and Ryo Moore
2020doi: 10.3934/dcds.2020131 +[Abstract](312) +[HTML](167) +[PDF](484.2KB)
Maximal equicontinuous generic factors and weak model sets
Gerhard Keller
2020doi: 10.3934/dcds.2020132 +[Abstract](235) +[HTML](156) +[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](242) +[HTML](157) +[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](284) +[HTML](174) +[PDF](394.63KB)
Gaussian iterative algorithm and integrated automorphism equation for random means
Justyna Jarczyk and Witold Jarczyk
2020doi: 10.3934/dcds.2020135 +[Abstract](241) +[HTML](162) +[PDF](293.27KB)
Entire and ancient solutions of a supercritical semilinear heat equation
Peter Poláčik and Pavol Quittner
2020doi: 10.3934/dcds.2020136 +[Abstract](305) +[HTML](155) +[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](368) +[HTML](180) +[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](501) +[HTML](163) +[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](217) +[HTML](137) +[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](156) +[HTML](104) +[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](171) +[HTML](120) +[PDF](534.48KB)
Euler integral and perihelion librations
Gabriella Pinzari
2020doi: 10.3934/dcds.2020165 +[Abstract](223) +[HTML](119) +[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](192) +[HTML](111) +[PDF](358.85KB)
Mean equicontinuity, complexity and applications
Jie Li, Xiangdong Ye and Tao Yu
2020doi: 10.3934/dcds.2020167 +[Abstract](227) +[HTML](128) +[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](219) +[HTML](119) +[PDF](620.02KB)
Time dependent center manifold in PDEs
Hongyu Cheng and Rafael de la Llave
2020doi: 10.3934/dcds.2020213 +[Abstract](70) +[HTML](41) +[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](55) +[HTML](37) +[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](112) +[HTML](37) +[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](67) +[HTML](32) +[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](59) +[HTML](27) +[PDF](702.9KB)
Minimal collision arcs asymptotic to central configurations
Vivina Barutello, Gian Marco Canneori and Susanna Terracini
2020doi: 10.3934/dcds.2020218 +[Abstract](83) +[HTML](33) +[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](84) +[HTML](51) +[PDF](771.22KB)
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](4201) +[PDF](233.8KB) Cited By(162)
Global attractors for damped semilinear wave equations
John M. Ball
2004, 10(1&2) : 31-52 doi: 10.3934/dcds.2004.10.31 +[Abstract](5325) +[PDF](246.2KB) Cited By(153)
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](5452) +[PDF](262.8KB) Cited By(142)
Remarks on regularities for the 3D MHD equations
Yong Zhou
2005, 12(5) : 881-886 doi: 10.3934/dcds.2005.12.881 +[Abstract](3114) +[PDF](176.3KB) Cited By(141)
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](5037) +[PDF](382.7KB) Cited By(133)
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](4411) +[PDF](369.4KB) Cited By(113)
Positive solution for a nonlinear stationary Schrödinger-Poisson system in $R^3$
Zhengping Wang and Huan-Song Zhou
2007, 18(4) : 809-816 doi: 10.3934/dcds.2007.18.809 +[Abstract](3201) +[PDF](153.0KB) Cited By(89)
BKM's criterion and global weak solutions for magnetohydrodynamics with zero viscosity
Zhen Lei and Yi Zhou
2009, 25(2) : 575-583 doi: 10.3934/dcds.2009.25.575 +[Abstract](3170) +[PDF](159.5KB) Cited By(82)
Global stability for damped Timoshenko systems
J.E. Muñoz Rivera and Reinhard Racke
2003, 9(6) : 1625-1639 doi: 10.3934/dcds.2003.9.1625 +[Abstract](3260) +[PDF](167.1KB) Cited By(76)
Attractors for nonautonomous 2d Navier-Stokes equations with normal external forces
Songsong Lu, Hongqing Wu and Chengkui Zhong
2005, 13(3) : 701-719 doi: 10.3934/dcds.2005.13.701 +[Abstract](3307) +[PDF](263.7KB) Cited By(74)
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
Wei Dai, Jiahui Huang, Yu Qin, Bo Wang and Yanqin Fang
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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
Anna Geyer and Ronald Quirchmayr
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Uniqueness of positive radial solutions of a semilinear elliptic equation in an annulus
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On the universality of the incompressible Euler equation on compact manifolds
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Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model
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Stability and bifurcation on predator-prey systems with nonlocal prey competition
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