Part 1 Basic Notions and Review
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 2 Low-Dimensional Models
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
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 Poincar~ Maps
5.1 Autonomous system of two coupled oscillators with self-regulating alternating excitation
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Part 3 Higher-Dimensional Systems and Phenomena
Part 4 Experimental Studies
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