A Vision for Dynamics in the 21st Century

Danijela Damjanovic is an Associate Professor at the Royal Institute of Technology (KTH), Sweden. She received her PhD in mathematics from Pennsylvania State University, USA in 2004. Her research is in the area of dynamics of smooth group actions. She serves on the editorial board of Journal of Modern Dynamics. Boris Hasselblatt is a professor at Tufts University, USA. He received his PhD from California Institute of Technology in 1989. He is a co-author of several books in the field of smooth dynamical systems, notably Introduction to the Modern Theory of Dynamical Systems. He is also (co-)editor of several large volumes, Handbook of Dynamical Systems, 1A and 1B, and The Collected Works of Anatole Katok, Volumes 1 and 2. He is Fellow and the Secretary of the American Mathematical Society. Andrey Gogolev is a Professor of Mathematics at The Ohio State University, USA. He received his PhD from Pennsylvania State University in 2009. His primary research interest is smooth dynamics with hyperbolic behavior. He serves on the editorial board of Journal of Modern Dynamics. Yakov Pesin is Distinguished Professor of Mathematics at Pennsylvania State University, USA. He is director of the Anatole Katok Center for Dynamical Systems and Geometry, a member of the American Academy of Arts and Sciences, a member of the European Academy (Academia Europea), a fellow of the American Mathematical Society, and an editor of the journal Ergodic Theory and Dynamical Systems. He received his PhD in mathematics from Gorky State University in 1979. He has (co)authored six books covering smooth dynamics, ergodic theory, dimension theory, and fractal geometry, and a dozen surveys on these topics.

• Editors note; 1. Rigidity of topological entropy of boundary maps associated to Fuchsian groups; 2. Open problems from 2020 vision for dynamics conference in Bedlewo; 3. Flexibility of entropies for piecewise expanding unimodalm maps; 4. Recent results and open questions on pseudo-rotations; 5. SRB and equilibrium measures via dimension theory; 6. Abelian Livshits theorems and geometric applications; 7. A dynamical approach to validated numerics; 8. Non-stationary normal forms for contracting extensions; 9. Survey on entropy-type invariants of sub-exponential growth in dynamical systems; 10. On the smooth realization problem and the AbC method; 11. On some spectral problems in ergodic theory; 12. Area preserving surface diffeomorphisms with polynomial decay of Correlation's are ubiquitous 13. Linear cocycles over hyperbolic systems.