exponential metric
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2022 ◽  
pp. 100946
Bobur Turimov ◽  
Yunus Turaev ◽  
Bobomurat Ahmedov ◽  
Zdeněk Stuchlík

2021 ◽  
Rakesh Kumar ◽  
Varun Joshi ◽  
Gaurav Dhiman ◽  
Wattana Viriyasitavat

2021 ◽  
Vol 0 (0) ◽  
Silas L. Carvalho ◽  
Alexander Condori

Abstract In this paper, we show that, for topological dynamical systems with a dense set (in the weak topology) of periodic measures, a typical (in Baire’s sense) invariant measure has, for each q > 0 {q>0} , zero lower q-generalized fractal dimension. This implies, in particular, that a typical invariant measure has zero upper Hausdorff dimension and zero lower rate of recurrence. Of special interest is the full-shift system ( X , T ) {(X,T)} (where X = M ℤ {X=M^{\mathbb{Z}}} is endowed with a sub-exponential metric and the alphabet M is a compact and perfect metric space), for which we show that a typical invariant measure has, for each q > 1 {q>1} , infinite upper q-correlation dimension. Under the same conditions, we show that a typical invariant measure has, for each s ∈ ( 0 , 1 ) {s\in(0,1)} and each q > 1 {q>1} , zero lower s-generalized and infinite upper q-generalized dimensions.

2020 ◽  
Vol 50 (11) ◽  
pp. 1346-1355 ◽  
Maxim Makukov ◽  
Eduard Mychelkin

2020 ◽  
Vol 20 (3) ◽  
pp. 391-400
Gauree Shanker ◽  
Kirandeep Kaur

AbstractWe prove the existence of an invariant vector field on a homogeneous Finsler space with exponential metric, and we derive an explicit formula for the S-curvature of a homogeneous Finsler space with exponential metric. Using this formula, we obtain a formula for the mean Berwald curvature of such a homogeneous Finsler space.

Universe ◽  
2020 ◽  
Vol 6 (1) ◽  
pp. 11 ◽  
Brandon Mattingly ◽  
Abinash Kar ◽  
William Julius ◽  
Matthew Gorban ◽  
Cooper Watson ◽  

The curvature invariants of three Lorentzian wormholes are calculated and plotted in this paper. The plots may be inspected for discontinuities to analyze the traversability of a wormhole. This approach was formulated by Henry, Overduin, and Wilcomb for black holes (Henry et al., 2016). Curvature invariants are independent of coordinate basis, so the process is free of coordinate mapping distortions and the same regardless of your chosen coordinates (Christoffel, E.B., 1869; Stephani, et al., 2003). The four independent Carminati and McLenaghan (CM) invariants are calculated and the nonzero curvature invariant functions are plotted (Carminati et al., 1991; Santosuosso et al., 1998). Three traversable wormhole line elements analyzed include the (i) spherically symmetric Morris and Thorne, (ii) thin-shell Schwarzschild wormholes, and (iii) the exponential metric (Visser, M., 1995; Boonserm et al., 2018).

2018 ◽  
Vol 98 (8) ◽  
Petarpa Boonserm ◽  
Tritos Ngampitipan ◽  
Alex Simpson ◽  
Matt Visser

2018 ◽  
Vol 10 (1) ◽  
pp. 167-177
Ramdayal Singh Kushwaha ◽  
Gauree Shanker

Abstract The (α, β)-metrics are the most studied Finsler metrics in Finsler geometry with Randers, Kropina and Matsumoto metrics being the most explored metrics in modern Finsler geometry. The ℒ-dual of Randers, Kropina and Matsumoto space have been introduced in [3, 4, 5], also in recent the ℒ-dual of a Finsler space with special (α, β)-metric and generalized Matsumoto spaces have been introduced in [16, 17]. In this paper, we find the ℒ-dual of a Finsler space with an exponential metric αeβ/α, where α is Riemannian metric and β is a non-zero one form.

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