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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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Renormalizing an infinite rational IET
W. Patrick Hooper1, Kasra Rafi and Anja Randecker
2020, 40(9) : 5105-5116 doi: 10.3934/dcds.2020220 +[Abstract](1) +[HTML](1) +[PDF](452.5KB)
Notes on the values of volume entropy of graphs
Wooyeon Kim and Seonhee Lim
2020, 40(9) : 5117-5129 doi: 10.3934/dcds.2020221 +[Abstract](1) +[HTML](3) +[PDF](363.85KB)
Exponential convergence in the Wasserstein metric $ W_1 $ for one dimensional diffusions
Lingyan Cheng, Ruinan Li and Liming Wu
2020, 40(9) : 5131-5148 doi: 10.3934/dcds.2020222 +[Abstract](1) +[HTML](2) +[PDF](390.07KB)
Contributions to the study of Anosov geodesic flows in non-compact manifolds
Ítalo Melo and Sergio Romaña
2020, 40(9) : 5149-5171 doi: 10.3934/dcds.2020223 +[Abstract](2) +[HTML](2) +[PDF](1021.13KB)
Limit theorems for additive functionals of path-dependent SDEs
Jianhai Bao, Feng-Yu Wang and Chenggui Yuan
2020, 40(9) : 5173-5188 doi: 10.3934/dcds.2020224 +[Abstract](3) +[HTML](2) +[PDF](359.87KB)
On the Cauchy problem for higher dimensional Benjamin-Ono and Zakharov-Kuznetsov equations
Robert Schippa
2020, 40(9) : 5189-5215 doi: 10.3934/dcds.2020225 +[Abstract](1) +[HTML](2) +[PDF](435.98KB)
A topological study of planar vector field singularities
Robert Roussarie
2020, 40(9) : 5217-5245 doi: 10.3934/dcds.2020226 +[Abstract](1) +[HTML](3) +[PDF](931.42KB)
Equidistribution of curves in homogeneous spaces and Dirichlet's approximation theorem for matrices
Nimish Shah and Lei Yang
2020, 40(9) : 5247-5287 doi: 10.3934/dcds.2020227 +[Abstract](1) +[HTML](2) +[PDF](580.95KB)
Interior and boundary regularity for the Navier-Stokes equations in the critical Lebesgue spaces
Hongjie Dong and Kunrui Wang
2020, 40(9) : 5289-5323 doi: 10.3934/dcds.2020228 +[Abstract](1) +[HTML](3) +[PDF](491.4KB)
Reducibility of quasi-periodically forced circle flows
Saša Kocić and João Lopes Dias
2020, 40(9) : 5325-5345 doi: 10.3934/dcds.2020229 +[Abstract](2) +[HTML](2) +[PDF](393.05KB)
Polynomial 3-mixing for smooth time-changes of horocycle flows
Adam Kanigowski and Davide Ravotti
2020, 40(9) : 5347-5371 doi: 10.3934/dcds.2020230 +[Abstract](2) +[HTML](2) +[PDF](504.61KB)
Liouville theorems on the upper half space
Lei Wang and Meijun Zhu
2020, 40(9) : 5373-5381 doi: 10.3934/dcds.2020231 +[Abstract](2) +[HTML](2) +[PDF](303.71KB)
Super fast vanishing solutions of the fast diffusion equation
Shu-Yu Hsu
2020, 40(9) : 5383-5414 doi: 10.3934/dcds.2020232 +[Abstract](1) +[HTML](3) +[PDF](439.27KB)
Time periodic solution to a coupled chemotaxis-fluid model withporous medium diffusion
Jiapeng Huang and Chunhua Jin
2020, 40(9) : 5415-5439 doi: 10.3934/dcds.2020233 +[Abstract](2) +[HTML](2) +[PDF](403.05KB)
Multiplicity of solutions for critical quasilinear Schrödinger equations using a linking structure
Edcarlos D. Silva and Jefferson S. Silva
2020, 40(9) : 5441-5470 doi: 10.3934/dcds.2020234 +[Abstract](1) +[HTML](3) +[PDF](414.4KB)
Global existence and convergence of nondimensionalized incompressible Navier-Stokes equations in low Froude number regime
Stefano Scrobogna
2020, 40(9) : 5471-5511 doi: 10.3934/dcds.2020235 +[Abstract](2) +[HTML](2) +[PDF](574.92KB)
Nonexistence of global solutions for the semilinear Moore – Gibson – Thompson equation in the conservative case
Wenhui Chen and Alessandro Palmieri
2020, 40(9) : 5513-5540 doi: 10.3934/dcds.2020236 +[Abstract](1) +[HTML](3) +[PDF](450.48KB)
Global existence and scattering of equivariant defocusing Chern-Simons-Schrödinger system
Jianjun Yuan
2020, 40(9) : 5541-5570 doi: 10.3934/dcds.2020237 +[Abstract](1) +[HTML](3) +[PDF](431.25KB)
Linearization of a nonautonomous unbounded system with nonuniform contraction: a spectral approach
Ignacio Huerta
2020, 40(9) : 5571-5590 doi: 10.3934/dcds.2020238 +[Abstract](2) +[HTML](2) +[PDF](431.37KB)
Infinitely many solutions for quasilinear equations with critical exponent and Hardy potential in $ \mathbb{R}^N $
Fengshuang Gao and Yuxia Guo
2020, 40(9) : 5591-5616 doi: 10.3934/dcds.2020239 +[Abstract](2) +[HTML](3) +[PDF](518.08KB)
Rigidity of random group actions
Woochul Jung, Keonhee Lee, Carlos Morales and Jumi Oh
2020doi: 10.3934/dcds.2020130 +[Abstract](386) +[HTML](205) +[PDF](292.41KB)
Generic Birkhoff spectra
Zoltán Buczolich, Balázs Maga and Ryo Moore
2020doi: 10.3934/dcds.2020131 +[Abstract](334) +[HTML](182) +[PDF](484.2KB)
Maximal equicontinuous generic factors and weak model sets
Gerhard Keller
2020doi: 10.3934/dcds.2020132 +[Abstract](246) +[HTML](166) +[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](259) +[HTML](175) +[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](303) +[HTML](187) +[PDF](394.63KB)
Gaussian iterative algorithm and integrated automorphism equation for random means
Justyna Jarczyk and Witold Jarczyk
2020doi: 10.3934/dcds.2020135 +[Abstract](255) +[HTML](173) +[PDF](293.27KB)
Entire and ancient solutions of a supercritical semilinear heat equation
Peter Poláčik and Pavol Quittner
2020doi: 10.3934/dcds.2020136 +[Abstract](317) +[HTML](166) +[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](385) +[HTML](191) +[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](522) +[HTML](174) +[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](239) +[HTML](149) +[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](171) +[HTML](115) +[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](183) +[HTML](131) +[PDF](534.48KB)
Euler integral and perihelion librations
Gabriella Pinzari
2020doi: 10.3934/dcds.2020165 +[Abstract](250) +[HTML](132) +[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](206) +[HTML](121) +[PDF](358.85KB)
Mean equicontinuity, complexity and applications
Jie Li, Xiangdong Ye and Tao Yu
2020doi: 10.3934/dcds.2020167 +[Abstract](242) +[HTML](141) +[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](242) +[HTML](127) +[PDF](620.02KB)
Time dependent center manifold in PDEs
Hongyu Cheng and Rafael de la Llave
2020doi: 10.3934/dcds.2020213 +[Abstract](89) +[HTML](56) +[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](71) +[HTML](52) +[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](140) +[HTML](53) +[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](80) +[HTML](47) +[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](79) +[HTML](41) +[PDF](702.9KB)
Minimal collision arcs asymptotic to central configurations
Vivina Barutello, Gian Marco Canneori and Susanna Terracini
2020doi: 10.3934/dcds.2020218 +[Abstract](103) +[HTML](48) +[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](138) +[HTML](67) +[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](4228) +[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](5349) +[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](5481) +[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](3141) +[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](5068) +[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](4433) +[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](3225) +[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](3188) +[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](3277) +[PDF](167.1KB) Cited By(76)
Attractors for nonautonomous 2d Navier-Stokes equations with normal external forces
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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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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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