Generalized dimensions of Feigenbaum's attractor from renormalization-group functional equations

A method is suggested for the computation of the generalized dimensions of fractal attractors at the period-doubling transition to chaos. The approach is based on an eigenvalue problem formulated in terms of functional equations, with a coefficient expressed in terms of Feigenbaum's universal fixed-point function. The accuracy of the results is determined only by precision of the representation of the universal function.Comment: 6 pages, 2 table

An Innovative Approach to Achieve Compositionality Efficiently using Multi-Version Object Based Transactional Systems

In the modern era of multicore processors, utilizing cores is a tedious job. Synchronization and communication among processors involve high cost. Software transaction memory systems (STMs) addresses this issues and provide better concurrency in which programmer need not have to worry about consistency issues. Another advantage of STMs is that they facilitate compositionality of concurrent programs with great ease. Different concurrent operations that need to be composed to form a single atomic unit is achieved by encapsulating them in a single transaction. In this paper, we introduce a new STM system as multi-version object based STM (MVOSTM) which is the combination of both of these ideas for harnessing greater concurrency in STMs. As the name suggests MVOSTM, works on a higher level and maintains multiple versions corresponding to each key. We have developed MVOSTM with the unlimited number of versions corresponding to each key. In addition to that, we have developed garbage collection for MVOSTM (MVOSTM-GC) to delete unwanted versions corresponding to the keys to reduce traversal overhead. MVOSTM provides greater concurrency while reducing the number of aborts and it ensures compositionality by making the transactions atomic. Here, we have used MVOSTM for the list and hash-table data structure as list-MVOSTM and HT- MVOSTM. Experimental results of list-MVOSTM outperform almost two to twenty fold speedup than existing state-of-the-art list based STMs (Trans-list, Boosting-list, NOrec-list, list-MVTO, and list-OSTM). HT-MVOSTM shows a significant performance gain of almost two to nineteen times better than existing state-of-the-art hash-table based STMs (ESTM, RWSTMs, HT-MVTO, and HT-OSTM). MVOSTM with list and hash-table shows the least number of aborts among all the existing STM algorithms. MVOSTM satisfies correctness-criteria as opacity.Comment: 35 pages, 23 figure

Hyperbolic Chaos of Turing Patterns

We consider time evolution of Turing patterns in an extended system governed by an equation of the Swift-Hohenberg type, where due to an external periodic parameter modulation long-wave and short-wave patterns with length scales related as 1:3 emerge in succession. We show theoretically and demonstrate numerically that the spatial phases of the patterns, being observed stroboscopically, are governed by an expanding circle map, so that the corresponding chaos of Turing patterns is hyperbolic, associated with a strange attractor of the Smale-Williams solenoid type. This chaos is shown to be robust with respect to variations of parameters and boundary conditions.Comment: 4 pages, 4 figure

Multistability and nonsmooth bifurcations in the quasiperiodically forced circle map

It is well-known that the dynamics of the Arnold circle map is phase-locked in regions of the parameter space called Arnold tongues. If the map is invertible, the only possible dynamics is either quasiperiodic motion, or phase-locked behavior with a unique attracting periodic orbit. Under the influence of quasiperiodic forcing the dynamics of the map changes dramatically. Inside the Arnold tongues open regions of multistability exist, and the parameter dependency of the dynamics becomes rather complex. This paper discusses the bifurcation structure inside the Arnold tongue with zero rotation number and includes a study of nonsmooth bifurcations that happen for large nonlinearity in the region with strange nonchaotic attractors.Comment: 25 pages, 22 colored figures in reduced quality, submitted to Int. J. of Bifurcation and Chaos, a supplementary website (http://www.mpipks-dresden.mpg.de/eprint/jwiersig/0004003/) is provide