Quick search Find article
Quick search
Find article

How projections affect the dimension spectrum of fractal measures

Brian R Hunt-+ and Vadim Yu Kaloshin++

Show affiliations


Recommended by P Grassberger

We introduce a new potential-theoretic definition of the dimension spectrum of a probability measure for q > 1 and explain its relation to prior definitions. We apply this definition to prove that if and is a Borel probability measure with compact support in , then under almost every linear transformation from to , the q-dimension of the image of is ; in particular, the q-dimension of is preserved provided . We also present results on the preservation of information dimension and pointwise dimension. Finally, for and q > 2 we give examples for which is not preserved by any linear transformation into . All results for typical linear transformations are also proved for typical (in the sense of prevalence) continuously differentiable functions.


PACS

05.45.Df Fractals

02.30.Cj Measure and integration

02.50.-r Probability theory, stochastic processes, and statistics

MSC

60B05 Probability measures on topological spaces

28A80 Fractals (See also 37Fxx)

37D45 Strange attractors, chaotic dynamics

Subjects

Mathematical physics

Computational physics

Statistical physics and nonlinear systems

Dates

Issue 5 (September 1997)

Received 8 January 1996, in final form 19 June 1997



  1. How projections affect the dimension spectrum of fractal measures

    Brian R Hunt and Vadim Yu Kaloshin 1997 Nonlinearity 10 1031

  2. A comparison of Monte Carlo dose calculation denoising techniques

    I El Naqa et al 2005 Phys. Med. Biol. 50 909

  3. Wannier function analysis of silicon–carbon alloys

    P Fitzhenry et al 2003 J. Phys.: Condens. Matter 15 165

  4. Gyrokinetic simulations of ETG and ITG turbulence

    A.M. Dimits et al 2007 Nucl. Fusion 47 817

  5. Magnetic penetration depth in unconventional superconductors

    Ruslan Prozorov and Russell W Giannetta 2006 Supercond. Sci. Technol. 19 R41

  6. Quantum–classical transition in scale relativity

    Marie-Noëlle Célérier and Laurent Nottale 2004 J. Phys. A: Math. Gen. 37 931

  7. The effect of local mild cold exposure on pulse transit time

    Xin-Yu Zhang and Yuan-Ting Zhang 2006 Physiol. Meas. 27 649

  8. On quantum Lie algebras and quantum root systems

    Gustav W Delius and Andreas Hüffmann 1996 J. Phys. A: Math. Gen. 29 1703

  9. New variables, the gravitational action and boosted quasilocal stress - energy - momentum

    Stephen R Lau 1996 Class. Quantum Grav. 13 1509

  10. The predictability problem in systems with an uncertainty in the evolution law

    G Boffetta et al 2000 J. Phys. A: Math. Gen. 33 1313

View by subject




Export








Please login to access our web services, or create an account if you don't yet have one.

You must have cookies enabled in your web browser to be able to login.

Username
Password

Forgotten your password? Get a new one here.