Last edited by Faera
Monday, July 20, 2020 | History

10 edition of Recurrences and discrete dynamic systems found in the catalog. # Recurrences and discrete dynamic systems

## by Igor Gumowski

Written in English

Subjects:
• Differentiable dynamical systems.,
• Point mappings (Mathematics)

• Edition Notes

Classifications The Physical Object Statement Igor Gumowski, Christian Mira. Series Lecture notes in mathematics ;, 809, Lecture notes in mathematics (Springer-Verlag) ;, 809. Contributions Mira, C., joint author. LC Classifications QA3 .L28 no. 809, QA614.8 .L28 no. 809 Pagination vi, 272 p. : Number of Pages 272 Open Library OL4105062M ISBN 10 0387100172 LC Control Number 80019718

Dynamical systems are about the evolution of some quantities over time. This evolution can occur smoothly over time or in discrete time steps. Here, we introduce dynamical systems where the state of the system evolves in discrete time steps, i.e., discrete dynamical systems. When we model a system as a discrete dynamical system, we imagine that we take a snapshot of the system at a . •The book begins with basic deﬁnitions and examples. Chapter 1 introduces the concepts of state vectors and divides the dynamical world into the discrete and the continuous. We then explore many instances of dynamical systems in the real world—our examples are drawn from physics, biology, economics, and numerical mathematics.

2 1. Basic Theory of Dynamical Systems A Simple Example. Let us start oﬀby examining a simple system that is mechanical in nature. We will have much more to say about examples of this sort later on. Basic mechanical examples are often grounded in New-ton’s law, F = ma. For now, we can think of a as simply the acceleration. Discrete & Continuous Dynamical Systems - B, , 20 (7): doi: /dcdsb  Luca Dieci, Cinzia Elia. Smooth to discontinuous systems: A geometric and numerical method for slow-fast dynamics.

The material on discrete dynamical systems starts with maps of one variable and proceeds to systems in higher dimensions. The treatment starts with examples where the periodic points can be found explicitly and then introduces symbolic dynamics to analyze where they can be shown to exist but not given in explicit form.   The second part of the book deals with discrete dynamical systems and progresses to the study of both continuous and discrete systems in contexts like chaos control and synchronization, neural networks, and binary oscillator computing. These later sections are useful reference material for undergraduate student projects. The book is rounded off.

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### Recurrences and discrete dynamic systems by Igor Gumowski Download PDF EPUB FB2

Recurrences and Discrete Dynamic Systems. Authors: Gumowski, Igor, Mira, Christian Free Preview. Genre/Form: Rekurrenz: Additional Physical Format: Online version: Gumowski, Igor.

Recurrences and discrete dynamic systems. Berlin ; New York: Springer-Verlag, Genre/Form: Electronic books: Additional Physical Format: Print version: Gumowski, Igor.

Recurrences and discrete dynamic systems. Berlin ; New York: Springer-Verlag. Igor Gumowski: free download. Ebooks library. On-line books store on Z-Library | B–OK. Download books for free. Find books. Cite this chapter as: Gumowski I., Mira C.

() Stochasticity in conservative recurrences. In: Recurrences and Discrete Dynamic Systems. Cite this chapter as: Gumowski I., Mira C.

() Some properties of second order recurrences. In: Recurrences and Discrete Dynamic Systems. Cite this chapter as: Gumowski I., Mira C. () Introduction and statement of the problem. In: Recurrences and Discrete Dynamic Systems. Gumowski I., Mira C.

() Stochasticity in almost conservative recurrences. In: Recurrences and Discrete Dynamic Systems. Lecture Notes in Mathematics, vol For measure preserving dynamical systems on metric spaces we study the time needed by a typical orbit to return back close to its starting point.

We prove that when the decay of correlation is super-polynomial the recurrence rates and the pointwise dimensions are equal. This gives a broad class of systems for which the recurrence rate equals the Hausdorff dimension of the invariant measure.

COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus.

Not Available Gumowski, I. /Mira, C., Recurrences and Discrete Dynamic Systems, Lecture Notes in MathematicsBerlin-Heidelberg-New York, Springer-VerlagVI.

Introduction. In a linear dynamical system, the variation of a state vector (an -dimensional vector denoted) equals a constant matrix (denoted) multiplied variation can take two forms: either as a flow, in which varies continuously with time = ⋅ ()or as a mapping, in which varies in discrete steps + = ⋅ These equations are linear in the following sense: if and () are two valid.

Author of World Scientific Series on Nonlinear Science, Series A, Vol Recurrences and Discrete Dynamic Systems, and Chaos in Discrete Dynamical Systems5/5(1). This book came recommended in Lay's Linear Algebra in the section on applications of eigenvalues to discrete dynamical systems.

I'm glad I bought it, like Lay's LA: it's very well written, proofs are rigorous yet easy to understand, examples are thoroughly explained, and most importantly the prose is informal and s: 6.

Gumowski, I. /Mira, C., Recurrences and Discrete Dynamic Systems, Lecture Notes in MathematicsBerlin‐Heidelberg‐New York, Springer‐VerlagVI, S.

conservative maps) of the book , and chapter 5 of the book . Gumowski I., Mira, C.: Recurrences and discrete dynamic systems - An introduction. We are going to try to solve these recurrence relations. By this we mean something very similar to solving differential equations: we want to find a function of \(n\) (a closed formula) which satisfies the recurrence relation, as well as the initial condition.

A dynamical system is a manifold M called the phase (or state) space endowed with a family of smooth evolution functions Φ t that for any element of t ∈ T, the time, map a point of the phase space back into the phase space. The notion of smoothness changes with applications and the type of manifold.

There are several choices for the set T is taken to be the reals, the dynamical. Spectra of dimensions for Poincaré recurrences. Discrete & Continuous Dynamical Systems - A,6 (4): doi: /dcds  V. Afraimovich, Jean-René Chazottes, Benoît Saussol.

Pointwise dimensions for Poincaré recurrences associated with maps and special flows.The convergence evaluation of the discrete linear quadratic regulator (DLQR) to map the Z-stable plane, is the main target of this research that is oriented to the development of tuning method for multivariable systems.

The tuning procedures is based on strategies to select the weighting matrices and dynamic programming. The solutions of DLQR are presented, since Bellman formulations until."Discrete dynamical systems are an interesting subject both for mathematicians and for applied scientists.

This book is an introduction to this topic. It consists of 6 chapters. The first one focuses on the analysis of the evolution of state variables in one dimensional first-order autonomous linear systems. The second chapter develops the Reviews: 1.