New Trends in Lyapunov Exponents

João Lopes Dias is an Associate Professor at ISEG - Universidade de Lisboa, Portugal. He did his PhD at the University of Cambridge, UK (2002) in the area of Hamiltonian dynamics and renormalization. His current research interests include topics on quasiperiodic motion, KAM theory, generic properties of dynamical systems and Lyapunov exponents.Pedro Miguel Duarte is an Associate Professor at Faculdade de Ciências -  Universidade de Lisboa, Portugal. He did his PhD at the  Institute of Pure and Applied Mathematics - IMPA, Brazil (1993). He does research on dynamical systems and ergodic theory, focusing on symplectic and conservative dynamics, random dynamical systems, billiards, evolutionary game dynamics  and linear cocycles.José Pedro Gaivão is an Assistant Professor at ISEG -  Universidade de Lisboa, Portugal. He did his PhD at the University of Warwick, UK (2010). He does research on dynamical systems and ergodic theory, focusing on symplectic and conservative dynamics, random dynamical systems and billiards.Silvius Klein is an Assistant Professor at the Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Brazil. He completed his PhD at the University of California, Los Angeles (UCLA) in 2005. He does research at the interface between dynamical systems and mathematical physics, focusing on statistical properties of linear cocycles and localization of discrete, ergodic Schrödinger operators.  Telmo Peixe is an Assistant Professor at ISEG - Universidade de Lisboa, Portugal. He did his PhD at the Universidade de Lisboa (2015), after getting a Master's degree from the same university. He does research on dynamical systems, focusing on differential equations and evolutionary game theory.Jaqueline Siqueira is an Assistant Professor at the Universidade Federal do Rio de Janeiro, Brazil. She did her PhD at the Universidade FederalFluminense, Brazil (2013). Her research area is dynamical systems with an emphasis on ergodic theory and, more particularly, on thermodynamic formalism.Maria Joana Torres is an Assistant Professor at Escola de Ciências - Universidade do Minho, Braga, Portugal. She did her PhD at the Universidade de Lisboa, Portugal (2004), after getting a Master's degree from the Universidade do Porto, Portugal. She does research on dynamical systems, focusing on symplectic and conservative dynamics, random dynamical systems, generic properties of dynamical systems and Lyapunov exponents.

• Preface.- Lyapunov Exponents for Linear Homogeneous Differential Equations.- An invitation to SL2(R) cocycles over random dynamics.- Randomness Versus Quasi-Periodicity.- Hyperbolicity or Zero Lyapunov Exponents for C2-Hamiltonians.- Generalized Lyapunov exponents and aspects of the theory of deep learning.- On the Multifractal Formalism of Lyapunov Exponents: A Survey of Recent Results.- The Continuity Problem of Lyapunov Exponents.- Some Questions and Remarks on Lyapunov Irregular Behavior for Linear Cocycles.