This text provides an accessible, self-contained and rigorous introduction to complex analysis and differential equations. Topics covered include holomorphic functions, Fourier series, ordinary and partial differential equations.
The text is divided into two parts: part one focuses on complex analysis and part two on differential equations. Each part can be read independently, so in essence this text offers two books in one. In the second part of the book, some emphasis is given to the application of complex analysis to differential equations. Half of the book consists of approximately...
This text provides an accessible, self-contained and rigorous introduction to complex analysis and differential equations. Topics covered include h...
The theory of dynamical systems is a broad and active research subject with connections to most parts of mathematics. "Dynamical Systems: An Introduction" undertakes the difficult task to provide a self-contained and compact introduction.
Topics covered include topological, low-dimensional, hyperbolic and symbolic dynamics, as well as a brief introduction to ergodic theory. In particular, the authors consider topological recurrence, topological entropy, homeomorphisms and diffeomorphisms of the circle, Sharkovski's ordering, the Poincare-Bendixson theory, and the construction of stable...
The theory of dynamical systems is a broad and active research subject with connections to most parts of mathematics. "Dynamical Systems: An Introd...
This book offers a unified introduction to the interplay of ergodic theory, hyperbolic dynamics, and dimension theory. Coverage includes intermediate level ergodic theory, thermodynamic formalism, or dimension theory of hyperbolic dynamics.
This book offers a unified introduction to the interplay of ergodic theory, hyperbolic dynamics, and dimension theory. Coverage includes intermediate ...
This book is the first comprehensive introduction to smooth ergodic theory. It consists of two parts: the first introduces the core of the theory and the second discusses more advanced topics. In particular, the book describes the general theory of Lyapunov exponents and its applications to the stability theory of differential equations, the concept of nonuniform hyperbolicity, stable manifold theory (with emphasis on absolute continuity of invariant foliations), and the ergodic theory of dynamical systems with nonzero Lyapunov exponents. A detailed description of all the basic examples of...
This book is the first comprehensive introduction to smooth ergodic theory. It consists of two parts: the first introduces the core of the theory and ...
This book is the first comprehensive introduction to smooth ergodic theory. It consists of two parts: the first introduces the core of the theory and the second discusses more advanced topics. In particular, the book describes the general theory of Lyapunov exponents and its applications to the stability theory of differential equations, the concept of nonuniform hyperbolicity, stable manifold theory (with emphasis on absolute continuity of invariant foliations), and the ergodic theory of dynamical systems with nonzero Lyapunov exponents. A detailed description of all the basic examples of...
This book is the first comprehensive introduction to smooth ergodic theory. It consists of two parts: the first introduces the core of the theory and ...
