A Contour Algorithm for Computing Stable Fiber Bundles of Nonautonomous, Noninvertible Maps
نویسنده
چکیده
Stable fiber bundles are the nonautonomous analog of stable manifolds and these objects provide valuable information on the underlying dynamics. We propose an algorithm for their computation that applies to a wide class of models, including noninvertible and nonautonomous discrete time systems. Precise error estimates are provided and fiber bundles are computed for several examples.
منابع مشابه
Computing stable hierarchies of fiber bundles
Stable fiber bundles are important structures for understanding nonautonomous dynamics. These sets have a hierarchical structure ranging from stable to strong stable fibers. First, we compute corresponding structures for linear systems and prove an error estimate. The spectral concept of choice is the Sacker-Sell spectrum that is based on exponential dichotomies. Secondly, we tackle the nonline...
متن کاملOn the Approximation of Stable and Unstable Fiber Bundles of (Non)Autonomous ODEs - A Contour Algorithm
We propose an algorithm for the approximation of stable and unstable fibers that applies to autonomous as well as to nonautonomous ODEs. The algorithm is based on computing the zero-contour of a specific operator; an idea that was introduced in [Hüls, 2014] for discrete time systems. We present precise error estimates for the resulting contour algorithm and demonstrate its efficiency by computi...
متن کاملm-SMOOTHNESS OF INVARIANT FIBER BUNDLES FOR DYNAMIC EQUATIONS ON MEASURE CHAINS
We present a new self-contained and rigorous proof of the smoothness of invariant fiber bundles for dynamic equations on measure chains or time scales. Here, an invariant fiber bundle is the generalization of an invariant manifold to the nonautonomous case. Our main result generalizes the “Hadamard-Perron theorem” to the time-dependent, infinitedimensional, noninvertible, and parameter-dependen...
متن کاملHomoclinic tangles for noninvertible maps
Not all naturally occurring iterated systems have the property that time is reversible. In which case, the dynamics must be modelled by a noninvertible map rather than by a di eomorphism. While one-dimensional theory describes dynamics of noninvertible maps, higher-dimensional theory has focussed on di eomorphisms, though there are many higher-dimensional examples of natural systems modelled by...
متن کاملNoninvertibility and “semi-” Analogs of (super) Manifolds, Fiber Bundles and Homotopies
Supersymmetry contains initially noninvertible objects, but it is common to deal with the invertible ones only, factorizing former in some extent. We propose to reconsider this ansatz and try to redefine such fundamental notions as supermanifolds, fiber bundles and homotopies using some weakening invertibility conditions. The prefix semireflects the fact that the underlying morphisms form corre...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Applied Dynamical Systems
دوره 15 شماره
صفحات -
تاریخ انتشار 2016