Kuznetsov博士是非线性和混沌动力学方面的著名科学家。他是俄罗斯萨拉托夫国立大学非线性过程系的教授，已经出版了三本混沌动力学及其应用方面的专著。

《双曲混沌(一个物理学家的观点)》是他的代表作之一，基于双曲混沌的特征，本书将展示如何找到物理系统中的双曲混沌吸引子，以及怎样设计具有双曲混沌的物理系统。

库兹涅佐夫所著的《双曲混沌(一个物理学家的观点)》从物理学而不是数学概念的角度介绍了目前动力系统中均匀双曲吸引子研究的进展小结构稳定的吸引子表现出强烈的随机性，但是对于动力系统中函数和参数的变化不敏感。基于双曲混沌的特征，本书将展示如何找到物理系统中的双曲混沌吸引子，以及怎样设计具有双曲混沌的物理系统。

《双曲混沌(一个物理学家的观点)》可以作为研究生和高年级本科生教材，也可以供大学教授以及物理学、机械学和工程学相关研究人员参考。

Part I Basic Notions and Review

 1 Dynamical Systems and Hyperbolicity

1.1 Dynamical systems： basic notions

 1.1.1 Systems with continuous and discrete time， and their mutual relation

 1.1.2 Dynamics in terms of phase fluid： Conservative and dissipative systems and attractors

 1.1.3 Rough systems and structural stability

 1.1.4 Lyapunov exponents and their computation

1.2 Model examples of chaotic attractors

 1.2.1 Chaos in terms of phase fluid and baker's map

 1.2.2 Smale-Williams solenoid

 1.2.3 DA-attractor

 1.2.4 Plykin type attractors

1.3 Notion of hyperbolicity

1.4 Content and conclusions of the hyperbolic theory

 1.4.1 Cone criterion

 1.4.2 Instability

 1.4.3 Transversal Cantor structure and Kaplan-Yorke dimension

 1.4.4 Markov partition and symbolic dynamics

 1.4.5 Enumerating of orbits and topological entropy

 1.4.6 Structural stability

 1.4.7 Invariant measure of Sinai-Ruelle-Bowen

 1.4.8 Shadowing and effect of noise

 1.4.9 Ergodicity and mixing

 1.4.10 Kolmogorov-Sinai entropy

References

 2 Possible Occurrence of Hyperbolic Attractors

2.1 The Newhouse-Ruelle-Takens theorem and its relation to the uniformly hyperbolic attractors

2.2 Lorenz model and its modifications

2.3 Some maps with uniformly hyperbolic attractors

2.4 From DA to the Plykin type attractor

2.5 Hunt's example： Suspending the Plykin type attractor

2.6 The triple linkage： A mechanical system with hyperbolic dynamics

2.7 A possible occurrence of a Plykin type attractor in Hindmarsh-Rose neuron model

2.8 Blue sky catastrophe and birth of the Smale-Williams attractor

2.9 Taffy-pulling machine

References

Part II Low-Dimensional Models

 3 Kicked Mechanical Models and Differential Equations with Periodic Switch

3.1 Smale-Williams solenoid in mechanical model： Motion of a particle on a plane under periodic kicks

3.2 A set of switching differential equations with attractor of Smale-Williams type

3.3 Explicit dynamical system with attractor of Plykin type

 3.3.1 Plykin type attractor on a sphere

 3.3.2 Plykin type attractor on the plane

3.4 Plykin-like attractor in smooth non-autonomous system

References

 4 Non-Autonomous Systems of Coupled Serf-Oscillators

4.1 Van der Pol oscillator

4.2 Smale-Williams attractor in a non-autonomous system of alternately excited van der Pol oscillators

4.3 System of alternately excited van der Pol oscillators in terms of slow complex amplitudes

4.4 Non-resonance excitation transfer

4.5 Plykin-like attractor in non-autonomous coupled oscillators

4.5.1 Representation of states on a sphere and equations of the model

4.5.2 Numerical results for the coupled oscillators

References

 5 Autonomous Low-dimensional Systems with Uniformly Hyperbolic Attractors in the Poincare Maps

5.1 Autonomous system of two coupled oscillators with self-regulating alternating excitation

5.2 System constructed on a base of the predator-prey model

5.3 Example of blue sky catastrophe accompanied by a birth of Smale-Williams attractor

References

 6 Parametric Generators of Hyperbolic Chaos

6.1 Parametric excitation of coupled oscillators. Three-frequency parametric generator and its operation

6.2 Hyperbolic chaos in parametric oscillator with Q-switch and pump modulation

 6.2.1 Dynamical equations

 6.2.2 Qualitative explanation of the operation

 6.2.3 Numerical results

 6.2.4 Numerical results in the frame of method of slow complex amplitudes

6.3 Parametric generator of hyperbolic chaos based on four coupled oscillators with pump modulation

 6.3.1 Model, operation principle and basic equations

 6.3.2 Chaotic dynamics: results of computer simulation

References

 7 Recognizing the Hyperbolicity: Cone Criterion and Other Approaches

7.1 Verification of transversality for manifolds

 7.1.1 Visualization of the manifolds

 7.1.2 Distributions of angles of the manifold intersections

7.2 Visualization of invariant measures

7.3 Cone criterion and examples of its application

 7.3.1 Procedure of verification of the cone criterion

 7.3.2 Examples of application of the cone criterion

References

Part III Higher-Dimensional Systems and Phenomena

 8 Systems of Four Alternately Excited Non-autonomous Oscillators

8.1 Arnold's cat map dynamics in a system of coupled

 non-autonomous van der Pol oscillators

8.2 Dynamics corresponding to hyperchaotic maps

 8.2.1 System implementing toral hyperchaotic map

 8.2.2 Model with cascade transfer of excitation upward the frequency spectrum

8.3 Hyperchaos and synchronous chaos in a system of coupled non-autonomous oscillators

 8.3.1 Equations and basic modes of operation

 8.3.2 Equations for slow complex amplitudes

References

 9 Autonomous Systems Based on Dynamics Close to Heteroclinic Cycle

9.1 Heteroclinic connection: an example of Guckenheimer and Holmes

9.2 Attractor of Smale-Williams type in a system of three coupled self-osciUators

9.3 Attractor with dynamics governed by the Arnold cat map

9.4 Model with hyperchaos

9.5 An autonomous system with attractor of Smale-Williams type

 with resonance transfer of excitation in a ring array of van der Pol oscillators

References

 10 Systems with Time-delay Feedback

10.1 Some notions concerning differential equations with deviating argument

10.2 Van der Pol oscillator with delayed feedback, parameter

 modulation and auxiliary signal

 10.2.1 Attractor of Smale-Williams type in the time-delayed system

 10.2.2 Hyperchaotic attractors

10.3 Van der Pol oscillator with two delayed feedback loops and parameter modulation

10.4 Autonomous time-delay system

References

 11 Chaos in Co-operative Dynamics of Alternately Synchronized

Ensembles of Globally Coupled Self-oscillators

11.1 Kuramoto transition in ensemble of globally coupled oscillators

11.2 Model of two alternately synchronized ensembles of oscillators

 11.2.1 Collective chaos in ensemble of van der Pol oscillators

 11.2.2 Slow-amplitude approach

 11.2.3 Description of the dynamics in terms of ensembles of phase oscillators

References

Part IV Experimental Studies

 12 Electronic Device with Attractor of Smale-Williams Type

12.1 Scheme of the device and the principle of operation

12.2 Experimental observation of the Smale-Williams attractor

References

 13 Delay-time Electronic Devices Generating Trains of Oscillations

with Phases Governed by Chaotic Maps

13.1 Van der Pol oscillator with delayed feedback, parameter

 modulation and auxiliary signal

13.2 Van der Pol oscillator with two delayed feedback loops and

 parameter modulation

References

 14 Conclusion

References

Appendix A Computation of Lyapunov Exponents: The Benettin Algorithm

 References

Appendix B Henon and Ikeda Maps

 References

Appendix C Smale's Horseshoe and Homoclinic Tangle

 References

Appendix D Fractal Dimensions and Kaplan-Yorke Formula

 References

Appendix E Hunt's Model: Formal Definition

 References

Appendix F Geodesics on a Compact Surface of Negative Curvature

 References

Appendix G Effect of Noise in a System with a Hyperbolic Attractor

 References

Index