Simple and complex dynamics for circle maps
نویسندگان
چکیده
منابع مشابه
Circle Maps as Simple Oscillators for Complex Behavior: I. Basics
The circle map and its basic properties as non-linear oscillator are discussed and related to other iterative mappings as proposed in the literature. The circle map is the simplest iterative generator for sustained periodic and chaotic sounds and is easy to interpret as a basic sine oscillator with a nonlinear perturbation.
متن کاملComplex Bounds for Critical Circle Maps
October 1995 Abstract. We use the methods developed with M. Lyubich for proving complex bounds for real quadratics to extend E. De Faria’s complex a priori bounds to all critical circle maps with an irrational rotation number. The contracting property for renormalizations of critical circle maps follows. In the Appendix we give an application of the complex bounds for proving local connectivity...
متن کاملCircle Maps as a Simple Oscillators for Complex Behavior: Ii. Experiments
The circle map is a general non-linear iterated function that maps the circle onto itself. In its standard form it can be interpreted as a simple sinusoidal oscillator which is perturbed by a non-linear term. By varying the strength of the non-linear contribution a rich array of non-linear responses can be achieved, including waveshaping, pitch-bending, period-doubling and highly irregular patt...
متن کاملComplex Bounds for Renormalization of Critical Circle Maps
We use the methods developed with M. Lyubich for proving complex bounds for real quadratics to extend E. De Faria's complex a priori bounds to all critical circle maps with an irrational rotation number. The contracting property for renormalizations of critical circle maps follows. As another application of our methods we present a new proof of theorem of C. Pe-tersen on local connectivity of s...
متن کاملPersistence for Circle Valued Maps
We study circle valued maps and consider the persistence of the homology of their fibers. The outcome is a finite collection of computable invariants which answer the basic questions on persistence and in addition encode the topology of the source space and its relevant subspaces. Unlike persistence of real valued maps, circle valued maps enjoy a different class of invariants called Jordan cell...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Publicacions Matemàtiques
سال: 1993
ISSN: 0214-1493
DOI: 10.5565/publmat_37293_05