This volume contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Relationships between Continuum Theory and the Theory of Dynamical Systems, held at Humboldt State University in Arcata, California in June 1989. The conference reflected recent interactions between dynamical systems and continuum theory. Illustrating the increasing confluence of these two areas, this volume contains introductory papers accessible to mathematicians and graduate students in any area of mathematics, as well as papers aimed more at specialists. Most of the papers are concerned with the dynamics of surface homeomorphisms or of continua that occur as attractors for surface homeomorphisms.

Based on the conference/workshop on Continuum Theory and Dynamical Systems held in Lafayette, Louisiana, this reference illustrates the current expansion of knowledge on the relationship between these subjects. It presents new problems in hyperspaces, induced maps, universal maps, fixed-point sets, disconnected numbers and quotient maps.;Explaining the definitions and techniques used in the two fields and providing results from both areas, this volume: examines prime end (accessible) rotation numbers for chaotic sets and Henon maps; discussed the connection between the rotation shadowing property and the structure of the rotation set for annulus homeomorphisms; offers a Nielson-type theorum concerning the minimum number of fixed points for an area preserving homeomorphism of the two disc; constructs a closed unit disc that admits many inequivalent homeomorphisms that are Denjoy on the boundary and distinct irrational rotations on the interior; gives a geometric description of a horseshoe-type mapping of a plane disc into itself whose attracting set is not chainable; and considers semigroups generated by maps topologically conjugate to contractions.;Written by experts who provide a cross-disciplinary perspective, this volume is intended for applied mathematicians, topologists, geomesters, physicists and graduate-level students in these disciplines.

This book presents a discussion of lattice dynamics for perfect and imperfect lattices and their relation to continuum theories of elasticity, piezoelectricity, viscoelasticity and plasticity. Some of the material is rather classical and close in spirit to solid state physics. A major aim here is to present a coherent theory for the four basic behavior types in the style of continuum mechanics. In each case, emphasis is on an explicit display of the physical mechanisms involved rather than general formalisms. The material is presented in terms of an atomistic picture for the discrete system. The basic ideas are believed to be relevant also at an intermediate scale in the continuum description of media with structure such as granular materials and composites.

Based on the conference/workshop on Continuum Theory and Dynamical Systems held in Lafayette, Louisiana, this reference illustrates the current expansion of knowledge on the relationship between these subjects. It presents new problems in hyperspaces, induced maps, universal maps, fixed-point sets, disconnected numbers and quotient maps.;Explaining the definitions and techniques used in the two fields and providing results from both areas, this volume: examines prime end (accessible) rotation numbers for chaotic sets and Henon maps; discussed the connection between the rotation shadowing property and the structure of the rotation set for annulus homeomorphisms; offers a Nielson-type theorum concerning the minimum number of fixed points for an area preserving homeomorphism of the two disc; constructs a closed unit disc that admits many inequivalent homeomorphisms that are Denjoy on the boundary and distinct irrational rotations on the interior; gives a geometric description of a horseshoe-type mapping of a plane disc into itself whose attracting set is not chainable; and considers semigroups generated by maps topologically conjugate to contractions.;Written by experts who provide a cross-disciplinary perspective, this volume is intended for applied mathematicians, topologists, geomesters, physicists and graduate-level students in these disciplines.

This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

A brand-new conceptual look at dynamical thermodynamics This book merges the two universalisms of thermodynamics and dynamical systems theory in a single compendium, with the latter providing an ideal language for the former, to develop a new and unique framework for dynamical thermodynamics. In particular, the book uses system-theoretic ideas to bring coherence, clarity, and precision to an important and poorly understood classical area of science. The dynamical systems formalism captures all of the key aspects of thermodynamics, including its fundamental laws, while providing a mathematically rigorous formulation for thermodynamical systems out of equilibrium by unifying the theory of mechanics with that of classical thermodynamics. This book includes topics on nonequilibrium irreversible thermodynamics, Boltzmann thermodynamics, mass-action kinetics and chemical reactions, finite-time thermodynamics, thermodynamic critical phenomena with continuous and discontinuous phase transitions, information theory, continuum and stochastic thermodynamics, and relativistic thermodynamics. A Dynamical Systems Theory of Thermodynamics develops a postmodern theory of thermodynamics as part of mathematical dynamical systems theory. The book establishes a clear nexus between thermodynamic irreversibility, the second law of thermodynamics, and the arrow of time to further unify discreteness and continuity, indeterminism and determinism, and quantum mechanics and general relativity in the pursuit of understanding the most fundamental property of the universe—the entropic arrow of time.

This volume contains the proceedings of the special session on Modern Methods in Continuum Theory presented at the 100th Annual Joint Mathematics Meetings held in Cincinnati, Ohio. It also features the Houston Problem Book which includes a recently updated set of 200 problems accumulated over several years at the University of Houston.;These proceedings and problems are aimed at pure and applied mathematicians, topologists, geometers, physicists and graduate-level students in these disciplines.