Structures in Dynamics: Finite Dimensional Deterministic StudiesThe study of non-linear dynamical systems nowadays is an intricate mixture of analysis, geometry, algebra and measure theory and this book takes all aspects into account. Presenting the contents of its authors' graduate courses in non-linear dynamical systems, this volume aims at researchers who wish to be acquainted with the more theoretical and fundamental subjects in non-linear dynamics and is designed to link the popular literature with research papers and monographs. All of the subjects covered in this book are extensively dealt with and presented in a pedagogic form. These include the presentation of an environment for the route to chaos by quasi-periodicity (which is related to the Landau-Lifschitz and Ruelle-Takens scenario's concerning the onset of turbulence); the theories of 1-dimensional dynamics, singularities in planar vector fields, and quasi-periodicity in dissipative systems. |
From inside the book
Results 1-3 of 32
... fixed point of f . If f ( J ) = J we can apply the argument above to f - 1 instead of ƒ , and conclude that the a - limit set of any orbit of ƒ is also a fixed point . If ƒ is orientation reversing ( that is , monotone decreasing ) ...
... fixed point ( x1 , ... , xk ) Є W , because then there exists a parameter μ such that ƒμ ( xi ) = x ( i ) and this implies that the forward orbits of the turning points of ƒ and g are ordered in the same way . Now the existence of such a ...
... fixed point p of fr : U → >> U in its interior then some iterate of T contains this fixed point of fr in its closure and since inf≥0 [ f * ( T ) | = 0 this fixed point of ƒ " must f " attract T and we are finished in this case . So we ...