Homoclinic bifurcations and dimension of attractors for damped nonlinear hyperbolic equations
- Turaev, Dmitry
- Zelik, Sergey
2010 Mathematics Subject Classification
- 35B41 37G20 35B45 37D45
- Damped hyperbolic equations, Global attractors, Homoclinic bifurcations, Lyapunov dimension, Fractal dimension
A new method of obtaining lower bounds for the attractor's dimension is suggested which involves analysis of homoclinic bifurcations. The method is applied for obtaining sharp estimates of the attractor's dimension for a class of abstract damped wave equations which are beyond the reach of the classical methods.