The aim of this monograph is to present a general method of proving continuity of Lyapunov exponents of linear cocycles. The method uses an inductive procedure based on a general, geometric version of the Avalanche Principle. The main assumption required by this method is the availability of appropriate large deviation type estimates for quantities related to the iterates of the base and fiber dynamics associated with the linear cocycle. We establish such estimates for various models of random and quasi-periodic cocycles. Our method has its origins in a paper of M. Goldstein and W. Schlag. Our present work expands upon their approach in both depth and breadth. We conclude this monograph with a list of related open problems, some of which may be treated using a similar approach.

Oceans and the Atmospheric Carbon Content, presents an interdisciplinary overview of the role of the oceans as a carbon sink and its relation with pH increasing trends and climate change. This volume discusses topics such as: climate variability during the last deglaciation, based on a high-resolution pollen analysis; the potential impact of CO2 from large metropolitan areas over the adjacent coastal zones and the importance of having high resolution atmospheric CO2 data to estimate accurately air-sea CO2 exchanges; present- day CO2 fluxes in the coastal ocean and their potential feedbacks under global climate change; phytoplankton community responses to climate change with emphasis on decreasing pH trends in sea water and its ecological effects; pH decrease and its effects on sea-water chemistry from a ten year time-series; the effect of acidification on metal bioaccumulation; the effects of increasing temperatures and acidification on contaminant dynamics and availability to biota; the prevention of potential environmental impacts related to the geological sequestration of CO2. The book provides an updated synthesis of current concerns related to global change trends in the oceans with a strong emphasis on acidification. The content draws attention to the importance of dealing with observed global change trends and their effects upon the oceans using an interdisciplinary approach due to their complexity and interlinks between different areas of knowledge.

This volume presents peer-reviewed surveys on new developments in the study of Lyapunov exponents in dynamical systems and its applications to other areas, such as mathematical physics. Written by leading experts in their fields, the contributions are based upon the presentations given by invited speakers at the “New Trends in Lyapunov Exponents� workshop held in Lisbon, Portugal, February 7–11, 2022. The works focus on the concept of Lyapunov exponents in their various manifestations in dynamical systems along with their applications to mathematical physics and other areas of mathematics. The papers reflect the spirit of the conference of promoting new connections among different subjects in dynamical systems. This volume aims primarily at researchers and graduate students working in dynamical systems and related fields, serving as an introduction to active fields of research and as a review of recent results as well.