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1.
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F 36
Feldman, David P. ,
Chaos and dynamical systems / / David P. Feldman. - Princeton : : Princeton University Press,, 2019. - 1 online resource (xiv, 245 pages) : : illustrations. - (Primers in complex systems). - Includes bibliographical references and index. - URL: https://library.dvfu.ru/lib/document/SK_ELIB/57DF9F8E-BD5C-4C91-8765-6F8A2E2E188D. - ISBN 9780691189390 (electronic bk.). - ISBN 0691189390 (electronic bk.)
Online resource; title from PDF title page (EBSCO, viewed June 5, 2019)
~РУБ DDC 514.742
Рубрики: Fractals.
Chaotic behavior in systems.
MATHEMATICS / Topology.
MATHEMATICS / General
Chaotic behavior in systems.
Fractals.
Аннотация: Chaos and Dynamical Systems presents an accessible, clear introduction to dynamical systems and chaos theory, an important and exciting area that has shaped many scientific fields. While the rules governing dynamical systems are well-specified and simple, the behavior of many dynamical systems is remarkably complex. Of particular note, simple deterministic dynamical systems produce output that appears random and for which long-term prediction is impossible. Using little math beyond basic algebra, David Feldman gives readers a grounded, concrete, and concise overview.In initial chapters, Feldman introduces iterated functions and differential equations. He then surveys the key concepts and results to emerge from dynamical systems: chaos and the butterfly effect, deterministic randomness, bifurcations, universality, phase space, and strange attractors. Throughout, Feldman examines possible scientific implications of these phenomena for the study of complex systems, highlighting the relationships between simplicity and complexity, order and disorder.Filling the gap between popular accounts of dynamical systems and chaos and textbooks aimed at physicists and mathematicians, Chaos and Dynamical Systems will be highly useful not only to students at the undergraduate and advanced levels, but also to researchers in the natural, social, and biological sciences.
F 36
Feldman, David P. ,
Chaos and dynamical systems / / David P. Feldman. - Princeton : : Princeton University Press,, 2019. - 1 online resource (xiv, 245 pages) : : illustrations. - (Primers in complex systems). - Includes bibliographical references and index. - URL: https://library.dvfu.ru/lib/document/SK_ELIB/57DF9F8E-BD5C-4C91-8765-6F8A2E2E188D. - ISBN 9780691189390 (electronic bk.). - ISBN 0691189390 (electronic bk.)
Online resource; title from PDF title page (EBSCO, viewed June 5, 2019)
Рубрики: Fractals.
Chaotic behavior in systems.
MATHEMATICS / Topology.
MATHEMATICS / General
Chaotic behavior in systems.
Fractals.
Аннотация: Chaos and Dynamical Systems presents an accessible, clear introduction to dynamical systems and chaos theory, an important and exciting area that has shaped many scientific fields. While the rules governing dynamical systems are well-specified and simple, the behavior of many dynamical systems is remarkably complex. Of particular note, simple deterministic dynamical systems produce output that appears random and for which long-term prediction is impossible. Using little math beyond basic algebra, David Feldman gives readers a grounded, concrete, and concise overview.In initial chapters, Feldman introduces iterated functions and differential equations. He then surveys the key concepts and results to emerge from dynamical systems: chaos and the butterfly effect, deterministic randomness, bifurcations, universality, phase space, and strange attractors. Throughout, Feldman examines possible scientific implications of these phenomena for the study of complex systems, highlighting the relationships between simplicity and complexity, order and disorder.Filling the gap between popular accounts of dynamical systems and chaos and textbooks aimed at physicists and mathematicians, Chaos and Dynamical Systems will be highly useful not only to students at the undergraduate and advanced levels, but also to researchers in the natural, social, and biological sciences.
2.
Подробнее
S 26
Saveliev, Nikolai.
Lectures on the Topology of 3-Manifolds [[electronic resource] :] : an Introduction to the Casson Invariant. / Nikolai. Saveliev. - 2nd ed. - Berlin : : De Gruyter,, 2011. - 1 online resource (219 p.). - URL: https://library.dvfu.ru/lib/document/SK_ELIB/A72DF210-A578-4828-A0E7-82EBF1FEF00A. - ISBN 9783110250367 (electronic bk.). - ISBN 3110250365 (e lectronic bk.)
Description based on print version record.
Параллельные издания: Print version: : Saveliev, Nikolai Lectures on the Topology of 3-Manifolds : An Introduction to the Casson Invariant. - Berlin : De Gruyter, c2011. - ISBN 9783110250350
Содержание:
Preface; Introduction; Glossary; 1 Heegaard splittings; 1.1 Introduction; 1.2 Existence of Heegaard splittings; 1.3 Stable equivalence of Heegaard splittings; 1.4 The mapping class group; 1.5 Manifolds of Heegaard genus <_ 1; 1.6 Seifert manifolds; 1.7 Heegaard diagrams; 1.8 Exercises; 2 Dehn surgery; 2.1 Knots and links in 3-manifolds; 2.2 Surgery on links in S3; 2.3 Surgery description of lens spaces and Seifert manifolds; 2.4 Surgery and 4-manifolds; 2.5 Exercises; 3 Kirby calculus; 3.1 The linking number; 3.2 Kirby moves; 3.3 The linking matrix; 3.4 Reversing orientation; 3.5 Exercises.
4 Even surgeries4.1 Exercises; 5 Review of 4-manifolds; 5.1 Definition of the intersection form; 5.2 The unimodular integral forms; 5.3 Four-manifolds and intersection forms; 5.4 Exercises; 6 Four-manifolds with boundary; 6.1 The intersection form; 6.2 Homology spheres via surgery on knots; 6.3 Seifert homology spheres; 6.4 The Rohlin invariant; 6.5 Exercises; 7 Invariants of knots and links; 7.1 Seifert surfaces; 7.2 Seifert matrices; 7.3 The Alexander polynomial; 7.4 Other invariants from Seifert surfaces; 7.5 Knots in homology spheres; 7.6 Boundary links and the Alexander polynomial.
7.7 Exercises8 Fibered knots; 8.1 The definition of a fibered knot; 8.2 The monodromy; 8.3 More about torus knots; 8.4 Joins; 8.5 The monodromy of torus knots; 8.6 Open book decompositions; 8.7 Exercises; 9 The Arf-invariant; 9.1 The Arf-invariant of a quadratic form; 9.2 The Arf-invariant of a knot; 9.3 Exercises; 10 Rohlin's theorem; 10.1 Characteristic surfaces; 10.2 The definition of q~; 10.3 Representing homology classes by surfaces; 11 The Rohlin invariant; 11.1 Definition of the Rohlin invariant; 11.2 The Rohlin invariant of Seifert spheres.
11.3 A surgery formula for the Rohlin invariant11.4 The homology cobordism group; 11.5 Exercises; 12 The Casson invariant; 12.1 Exercises; 13 The group SU (2); 13.1 Exercises; 14 Representation spaces; 14.1 The topology of representation spaces; 14.2 Irreducible representations; 14.3 Representations of free groups; 14.4 Representations of surface groups; 14.5 Representations for Seifert homology spheres; 14.6 Exercises; 15 The local properties of representation spaces; 15.1 Exercises; 16 Casson's invariant for Heegaard splittings; 16.1 The intersection product; 16.2 The orientations.
16.3 Independence of Heegaard splitting16.4 Exercises; 17 Casson's invariant for knots; 17.1 Preferred Heegaard splittings; 17.2 The Casson invariant for knots; 17.3 The difference cycle; 17.4 The Casson invariant for boundary links; 17.5 The Casson invariant of a trefoil; 18 An application of the Casson invariant; 18.1 Triangulating 4-manifolds; 18.2 Higher-dimensional manifolds; 18.3 Exercises; 19 The Casson invariant of Seifert manifolds; 19.1 The space R(S (p, q, r)); 19.2 Calculation of the Casson invariant; 19.3 Exercises; Conclusion; Bibliography; Index.
~РУБ DDC 514.34
Рубрики: Homology.
Physics.
Three-manifolds (Topology)
Mathematics.
Three-manifolds (Topology)
MATHEMATICS / Topology
Аннотация: This textbook, now in its second revised and extended edition, introduces the topology of 3- and 4-dimensional manifolds. It also considers new developments especially related to the Heegaard Floer and contact homology. The book is accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic topology, including the fundamental group, basic homology theory, and Poincaré duality on manifolds.
S 26
Saveliev, Nikolai.
Lectures on the Topology of 3-Manifolds [[electronic resource] :] : an Introduction to the Casson Invariant. / Nikolai. Saveliev. - 2nd ed. - Berlin : : De Gruyter,, 2011. - 1 online resource (219 p.). - URL: https://library.dvfu.ru/lib/document/SK_ELIB/A72DF210-A578-4828-A0E7-82EBF1FEF00A. - ISBN 9783110250367 (electronic bk.). - ISBN 3110250365 (e lectronic bk.)
Description based on print version record.
Параллельные издания: Print version: : Saveliev, Nikolai Lectures on the Topology of 3-Manifolds : An Introduction to the Casson Invariant. - Berlin : De Gruyter, c2011. - ISBN 9783110250350
Содержание:
Preface; Introduction; Glossary; 1 Heegaard splittings; 1.1 Introduction; 1.2 Existence of Heegaard splittings; 1.3 Stable equivalence of Heegaard splittings; 1.4 The mapping class group; 1.5 Manifolds of Heegaard genus <_ 1; 1.6 Seifert manifolds; 1.7 Heegaard diagrams; 1.8 Exercises; 2 Dehn surgery; 2.1 Knots and links in 3-manifolds; 2.2 Surgery on links in S3; 2.3 Surgery description of lens spaces and Seifert manifolds; 2.4 Surgery and 4-manifolds; 2.5 Exercises; 3 Kirby calculus; 3.1 The linking number; 3.2 Kirby moves; 3.3 The linking matrix; 3.4 Reversing orientation; 3.5 Exercises.
4 Even surgeries4.1 Exercises; 5 Review of 4-manifolds; 5.1 Definition of the intersection form; 5.2 The unimodular integral forms; 5.3 Four-manifolds and intersection forms; 5.4 Exercises; 6 Four-manifolds with boundary; 6.1 The intersection form; 6.2 Homology spheres via surgery on knots; 6.3 Seifert homology spheres; 6.4 The Rohlin invariant; 6.5 Exercises; 7 Invariants of knots and links; 7.1 Seifert surfaces; 7.2 Seifert matrices; 7.3 The Alexander polynomial; 7.4 Other invariants from Seifert surfaces; 7.5 Knots in homology spheres; 7.6 Boundary links and the Alexander polynomial.
7.7 Exercises8 Fibered knots; 8.1 The definition of a fibered knot; 8.2 The monodromy; 8.3 More about torus knots; 8.4 Joins; 8.5 The monodromy of torus knots; 8.6 Open book decompositions; 8.7 Exercises; 9 The Arf-invariant; 9.1 The Arf-invariant of a quadratic form; 9.2 The Arf-invariant of a knot; 9.3 Exercises; 10 Rohlin's theorem; 10.1 Characteristic surfaces; 10.2 The definition of q~; 10.3 Representing homology classes by surfaces; 11 The Rohlin invariant; 11.1 Definition of the Rohlin invariant; 11.2 The Rohlin invariant of Seifert spheres.
11.3 A surgery formula for the Rohlin invariant11.4 The homology cobordism group; 11.5 Exercises; 12 The Casson invariant; 12.1 Exercises; 13 The group SU (2); 13.1 Exercises; 14 Representation spaces; 14.1 The topology of representation spaces; 14.2 Irreducible representations; 14.3 Representations of free groups; 14.4 Representations of surface groups; 14.5 Representations for Seifert homology spheres; 14.6 Exercises; 15 The local properties of representation spaces; 15.1 Exercises; 16 Casson's invariant for Heegaard splittings; 16.1 The intersection product; 16.2 The orientations.
16.3 Independence of Heegaard splitting16.4 Exercises; 17 Casson's invariant for knots; 17.1 Preferred Heegaard splittings; 17.2 The Casson invariant for knots; 17.3 The difference cycle; 17.4 The Casson invariant for boundary links; 17.5 The Casson invariant of a trefoil; 18 An application of the Casson invariant; 18.1 Triangulating 4-manifolds; 18.2 Higher-dimensional manifolds; 18.3 Exercises; 19 The Casson invariant of Seifert manifolds; 19.1 The space R(S (p, q, r)); 19.2 Calculation of the Casson invariant; 19.3 Exercises; Conclusion; Bibliography; Index.
Рубрики: Homology.
Physics.
Three-manifolds (Topology)
Mathematics.
Three-manifolds (Topology)
MATHEMATICS / Topology
Аннотация: This textbook, now in its second revised and extended edition, introduces the topology of 3- and 4-dimensional manifolds. It also considers new developments especially related to the Heegaard Floer and contact homology. The book is accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic topology, including the fundamental group, basic homology theory, and Poincaré duality on manifolds.
3.
Подробнее
B 96
Burde, Gerhard, (1931-).
Knots [[electronic resource].] / Gerhard, Burde ; author.: Zieschang, Heiner,, Heusener, Michael,. - 3rd [edition] /, by Gerhard Burde, Heiner Zieschang, Michael Heusener. - Berlin ; ; Boston : : Walter de Gruyter GmbH & Co. KG,, 2013. - 1 online resource (pages cm.). - Includes bibliographical references and index. - URL: https://library.dvfu.ru/lib/document/SK_ELIB/1D599B77-3414-4206-8679-BAEBB56EA8D4. - ISBN 3110270781 (e lectronic bk.). - ISBN 9783110270785 (electronic bk.)
Description based on print version record.
Параллельные издания: Print version: :
~РУБ DDC 514/.2242
Рубрики: Knot theory.
MATHEMATICS / Topology
Доп.точки доступа:
Zieschang, Heiner, \author.\
Heusener, Michael, \author.\
B 96
Burde, Gerhard, (1931-).
Knots [[electronic resource].] / Gerhard, Burde ; author.: Zieschang, Heiner,, Heusener, Michael,. - 3rd [edition] /, by Gerhard Burde, Heiner Zieschang, Michael Heusener. - Berlin ; ; Boston : : Walter de Gruyter GmbH & Co. KG,, 2013. - 1 online resource (pages cm.). - Includes bibliographical references and index. - URL: https://library.dvfu.ru/lib/document/SK_ELIB/1D599B77-3414-4206-8679-BAEBB56EA8D4. - ISBN 3110270781 (e lectronic bk.). - ISBN 9783110270785 (electronic bk.)
Description based on print version record.
Параллельные издания: Print version: :
Рубрики: Knot theory.
MATHEMATICS / Topology
Доп.точки доступа:
Zieschang, Heiner, \author.\
Heusener, Michael, \author.\
4.
Подробнее
K 62
Knots, Groups and 3-Manifolds : : Papers Dedicated to the Memory of R.H. Fox / / edited by L.P. Neuwirth. - New Jersey : : Princeton University Press,, ©1975. - 1 online resource : : illustrations. - (Annals of Mathematics Studies ; ; number 84). - Includes bibliographical references. - URL: https://library.dvfu.ru/lib/document/SK_ELIB/D7EEE89E-2CEF-469D-BFEA-7CB6DBDCB17F. - ISBN 9781400881512 (electronic bk.). - ISBN 140088151X (electronic bk.)
Online resource; title from PDF title page (EBSCO, viewed April 20, 2017).
~РУБ DDC 514.2242
Рубрики: Knot theory.
Group theory.
Three-manifolds (Topology)
MATHEMATICS / Topology
Group theory.
Knot theory.
Three-manifolds (Topology)
Доп.точки доступа:
Neuwirth, L. P., (Lee Paul)
K 62
Knots, Groups and 3-Manifolds : : Papers Dedicated to the Memory of R.H. Fox / / edited by L.P. Neuwirth. - New Jersey : : Princeton University Press,, ©1975. - 1 online resource : : illustrations. - (Annals of Mathematics Studies ; ; number 84). - Includes bibliographical references. - URL: https://library.dvfu.ru/lib/document/SK_ELIB/D7EEE89E-2CEF-469D-BFEA-7CB6DBDCB17F. - ISBN 9781400881512 (electronic bk.). - ISBN 140088151X (electronic bk.)
Online resource; title from PDF title page (EBSCO, viewed April 20, 2017).
Рубрики: Knot theory.
Group theory.
Three-manifolds (Topology)
MATHEMATICS / Topology
Group theory.
Knot theory.
Three-manifolds (Topology)
Доп.точки доступа:
Neuwirth, L. P., (Lee Paul)
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