Nicolau Corção Saldanha

Publications

This is a list of my mathematical writings, whether actually published or just made public as some sort of preprint. Anything that has been published is indicated with reference. You may download TeX sources, postscript files and pdf files. If you prefer, you may view the papers as png files. Some publications (but not all) are also available in html format. Files are compressed with gzip and some browsers will uncompress them automatically but others will not; some will uncompress the file but not remove the .gz extention and thus confuse the user or other programs. If you cannot print or display the files as you get them, you may need to decompress them manually with gunzip.

Please consider anything you get here as an informal preprint obtained at personal request. Thus, you will find preliminary versions of some papers and partial copies of others (e.g., without the figures). The ``official'' version is what you see published on paper.

Please write to nicolau AT mat.puc-rio.br if you have any difficulties downloading documents.


Topology

Homotopy type of spaces of curves with constrained curvature on flat surfaces

With Pedro Zühlke.

Also at http://www.arxiv.org/abs/1410.8590.

flatpathsII.tgz flatpathsII.ps.gz flatpathsII.pdf view png

Components of spaces of curves with constrained curvature on flat surfaces

With Pedro Zühlke. To appear in Pacific Journal of Mathematics.

Also at http://www.arxiv.org/abs/1312.1675.

flatpa/ddithsI.tgz flatpathsI.ps.gz flatpathsI.pdf view png

On The Components of Spaces of Curves on the 2-Sphere with Geodesic Curvature in a Prescribed Interval

With Pedro Zühlke. International Journal of Mathematics, Vol. 24, No. 14 (2013) 1350101 (78 pages).
doi:10.1142/S0129167X13501012

Also at http://www.arxiv.org/abs/1304.2629.

homotopies.tgz homotopies.ps.gz homotopies.pdf view png

The homotopy type of spaces of locally convex curves in the sphere

Geometry and Topology 19 (2015) 1155-1203; DOI: 10.2140/gt.2015.19.1155.
Also at http://www.arxiv.org/abs/1207.4221.

onion.tgz onion.ps.gz onion.pdf view png

The homotopy and cohomology of spaces of locally convex curves in the sphere --- I

Also at http://www.arxiv.org/abs/0905.2111.

flower.tgz flower.ps.gz flower.pdf view png

The homotopy and cohomology of spaces of locally convex curves in the sphere --- II

Also at http://www.arxiv.org/abs/0905.2116.

osculating.tgz osculating.ps.gz osculating.pdf view png

Spaces of locally convex curves in S^n and combinatorics of the group B^+_{n+1}

With Boris Shapiro. Journal of Singularities, 4, 1-22, 2012. Also at http://www.arxiv.org/abs/math/0703803.

sasha.tgz sasha.ps.gz sasha.pdf view png

Stability of compact actions of the Heisenberg group

With Tania M. Begazo. Also at http://www.arxiv.org/abs/math.GT/0412501.

heisenberg.tex.gz heisenberg.ps.gz heisenberg.pdf view png

Homotopy and cohomology of spaces of locally convex curves in the sphere

Also at http://www.arxiv.org/abs/math.GT/0407410.

convex.tgz convex.ps.gz convex.pdf view png

Nilpotent pseudogroups of functions on an interval

With Tania M. Begazo. Bull Braz Math Soc, New Series 36(1), 25-38 (2005). Also at http://www.arxiv.org/abs/math.DS/0404157.

uninil.tex.gz uninil.ps.gz uninil.pdf view png

Stability of compact actions of Rn of codimension one

Comment. Math. Helvetici, 69, 431-446 (1994).

stable.tar.gz stable.ps.gz stable.pdf view png

Actions of Rn over Tn-fibrations

Preprint.

torus.tar.gz torus.ps.gz torus.pdf view png

An introduction to geometric topology: Geometric Structures on 2 and 3-Manifolds

Contemporary Mathematics, vol. 161 (Differential Topology, Foliations, and Group Actions), 1994.

workshop.tar.gz workshop.ps.gz workshop.pdf view png


Differential equations

The geometry of the critical set of nonlinear periodic Sturm-Liouville operators

With Dan Burghelea and Carlos Tomei. J. Differential Equations 246, 3380-3397 (2009). doi:10.1016/j.jde.2008.10.021

Also at http://arxiv.org/abs/0707.1256

periodic.tar.gz periodic.ps.gz periodic.pdf view png

The topology of the monodromy map of a second order ODE

With Dan Burghelea and Carlos Tomei. J. Differential Equations 227, 581-597 (2006).

Also at http://www.arxiv.org/abs/math.CA/0507120

monodromy.tar.gz monodromy.ps.gz monodromy.pdf view png

The topology of critical sets of some ordinary differential operators

With Carlos Tomei. Progress in Nonlinear Differential Equations and Their Applications, Vol. 66, 491-504 (2005).

Also at http://www.arxiv.org/abs/math.FA/0501071

djairo.tar.gz djairo.ps.gz djairo.pdf view png

Results on infinite dimensional topology and applications to the structure of the critical set of nonlinear Sturm-Liouville operators

With Dan Burghelea and Carlos Tomei. J. Differential Equations 188, 569-590 (2003).

Also at http://www.arxiv.org/abs/math.FA/0107197

bbst.tar.gz bbst.ps.gz bbst.pdf view png

Morin singularities and global geometry in a class of ordinary differential operators

With Iaci Malta and Carlos Tomei. Topological Methods in Non-linear analysis, 10:137-169 (1997).

mstedo.tar.gz mstedo.ps.gz mstedo.pdf view png

The version above incorporates corrections to the original version of the paper. See below the errata as published in TMNA.

With Carlos Tomei. Topological Methods in Non-linear analysis, 32:411-414 (2008).

mstedo-errata.tar.gz mstedo-errata.ps.gz mstedo-errata.pdf view png

The paper above received a Featured Review from Math Reviews.

Regular level sets of averages of Nemytskii operators are contractible

With Iaci Malta and Carlos Tomei. Journal of Functional Analysis, 143, no. 2, 461-469 (1997).

contract.tar.gz contract.ps.gz contract.pdf view png


Linear algebra and spectral theory

Dynamics of the symmetric eigenvalue problem with shift strategies

With Ricardo S. Leite and Carlos Tomei. International Mathematics Research Notices 2012; doi: 10.1093/imrn/rns186

Also at http://arxiv.org/abs/1108.6030.

weakap.tar.gz weakap.ps.gz weakap.pdf view png

The Asymptotics of Wilkinson's Iteration: Loss of Cubic Convergence

With Ricardo S. Leite and Carlos Tomei. Foundations of Computational Mathematics, 10 (1), 15-36, 2010. doi:10.1007/s10208-009-9047-3

Also at http://www.arxiv.org/abs/0807.0415.

cubicloss.tar.gz cubicloss.ps.gz cubicloss.pdf view png

An atlas for tridiagonal isospectral manifolds

With Ricardo S. Leite and Carlos Tomei. Linear Algebra and Applications, vol. 429, 387-402 (2008). doi:10.1016/j.laa.2008.03.001

Also at http://www.arxiv.org/abs/math.SP/0608558.

bidiagonal.tar.gz bidiagonal.ps.gz bidiagonal.pdf view png

Reconstruction of tridiagonal matrices from spectral data

With Ricardo S. Leite and Carlos Tomei. Also at http://www.arxiv.org/abs/math.NA/0508099.

invbi.tar.gz invbi.ps.gz invbi.pdf view png

The asymptotics of Wilkinson's shift iteration

With Ricardo S. Leite and Carlos Tomei. Also at http://www.arxiv.org/abs/math.NA/0412493.

conjetura.tar.gz conjetura.ps.gz conjetura.pdf view png

The Accumulated Distribution of Quadratic Forms on the Sphere

With Carlos Tomei. Linear Algebra and Applications, vol. 245, 335-351 (1996).

quad.tar.gz quad.ps.gz quad.pdf view png


Tilings

Domino tilings of three-dimensional regions: flips, trits and twists

With Pedro Milet. At http://arxiv.org/abs/1410.7693.

multiplex.tar.gz multiplex.ps.gz multiplex.pdf view png

See also additional material elsewhere.

Twists for duplex regions

With Pedro Milet. At http://arxiv.org/abs/1411.1793.

twist.tar.gz twist.ps.gz twist.pdf view png

Flip invariance for domino tilings of three-dimensional regions with two floors

With Pedro Milet.
Discrete Comput Geom (2015) 53:914-940; DOI 10.1007/s00454-015-9685-y.
At http://arxiv.org/abs/1404.6509.

twofloor.tar.gz twofloor.ps.gz twofloor.pdf view png

Cut-and-paste of quadriculated disks and arithmetic properties of the adjacency matrix

With Carlos Tomei. Linear Algebra and Applications, vol. 432, 2423-2437 (2010). doi:10.1016/j.laa.2009.09.003

Also at http://arxiv.org/abs/0904.4814. There is an older preprint covering part of the material here: http://www.arxiv.org/abs/math.CO/0107162.

disk.tar.gz disk.ps.gz disk.pdf view png

Tilings of quadriculated annuli

With Carlos Tomei. Journal of Combinatorial Theory, Series B 88 (2003) 153-183.

Also at http://www.arxiv.org/abs/math.CO/0012265

annuli.tar.gz annuli.ps.gz annuli.pdf view png

Singular polynomials of generalized Kasteleyn matrices

Journal of Algebraic Combinatorics, 16(2): 195-207, (2002).

Also at http://www.arxiv.org/abs/math.CO/0101002

kk.tar.gz kk.ps.gz kk.pdf view png

Spaces of domino tilings

With Carlos Tomei, Mario Casarin and Domingos Romualdo. Discrete Comput. Geom. 14:207-233 (1995).

domino.tar.gz domino.ps.gz domino.pdf view png

An overview of domino and lozenge tilings

With Carlos Tomei. Resenhas IME-USP, 2(2), 239-252, (1995).

Also at http://www.arxiv.org/abs/math.CO/9801111

resenhas.tar.gz resenhas.ps.gz resenhas.pdf view png

Some remarks on self-affine tilings

With Derek Hacon and J. J. P. Veerman. Experimental Mathematics, 3, 317-327 (1994).

hsv.tar.gz hsv.ps.gz hsv.pdf view png

Two results on tilings of quadriculated annuli

With Carlos Tomei. Preprint.

Also at http://www.arxiv.org/abs/math.CO/0102027

miniannuli.tar.gz miniannuli.ps.gz miniannuli.pdf view png


Polytopes

Spectra of semi-regular polytopes

With Carlos Tomei. Boletim da Sociedade Brasileira de Matemática, vol. 29, n. 1, 25-51 (1998).

Also at http://www.arxiv.org/abs/math.CO/9712252

semi.tar.gz semi.ps.gz semi.pdf view png

Spectra of regular polytopes

With Carlos Tomei. Discrete Comput. Geom. 7:403-414 (1992).

poly.tar.gz poly.ps.gz poly.pdf view png


Functions in the plane

Functions from R2 to R2: a study in nonlinearity

With Carlos Tomei.

Also at http://www.arxiv.org/abs/math.NA/0209097

rouche.tar.gz rouche.ps.gz rouche.pdf view png

The numerical inversion of functions from the plane to the plane

With Iaci Malta and Carlos Tomei. Mathematics of Computation 65, no. 216, 1531-1552 (1996).

mst.tar.gz mst.ps.gz mst.pdf view png

Critical sets of proper Whitney functions in the plane

With Iaci Malta and Carlos Tomei. Matemática Contemporânea, SBM, vol. 13, 10th Brazilian Topology Meeting, 181-228 (1997).

topology.tar.gz topology.ps.gz topology.pdf view png

On the problem of solving F(x) = y in the plane

With Iaci Malta and Carlos Tomei. Matemática Contemporânea, SBM, vol. 3, 89-107 (1992).

fxybis.tar.gz fxybis.ps.gz fxybis.pdf view png


Editor

Foliations, Geometry, and Topology: Paul Schweitzer Festschrift

Editors: Nicolau C. Saldanha, Lawrence Conlon, Rémi Langevin, Takashi Tsuboi, Pawel Walczak;
AMS, 2009, 232 pp., ISBN-10: 0-8218-4628-0, ISBN-13: 978-0-8218-4628-5, CONM/498.


Books

Teoria dos números: um passeio com primos e outros números familiares pelo mundo inteiro

In portuguese. With Fabio Brochero Martinez, Carlos G. Moreira and Eduardo Tengan.
ISBN: 978-85-244-0312-5, Projeto Euclides, Impa, 2010.

The eletronic version is not available yet. The book can be bought from IMPA.

Olimpíadas Brasileiras de Matemática, 9a a 16a, Problemas e resoluções

In portuguese. With Carlos G. Moreira, Edmilson Motta, Eduardo Tengan, Luiz Amâncio and Paulo Rodrigues.
ISBN 85-85818-19-0, Sociedade Brasileira de Matemática, Rio de Janeiro, 2003.

The eletronic version is not available yet. The book can be bought from SBM.

Tópicos em Matemática Quântica

In portuguese. With Derek Hacon, George Svetlichny, Carlos Tomei and Paulo Viana. Course text for the 22th Colóquio Brasileiro de Matemática, IMPA, 1999.

q.tar.gz q.ps.gz q.pdf view png

Primos de Mersenne (e outros primos muito grandes)

In portuguese. With Carlos Gustavo T. de A. Moreira. Course text for the 22th Colóquio Brasileiro de Matemática, IMPA, 1999.

mersenne.tar.gz mersenne.ps.gz mersenne.pdf view png

Funções do plano no plano

In portuguese. With Iaci Malta and Carlos Tomei. Course text for the 19th Colóquio Brasileiro de Matemática, IMPA, 1993.

colo.tar.gz colo.ps.gz colo.pdf view png

Tópicos em Jogos Combinatórios

In portuguese. Course text for the 18th Colóquio Brasileiro de Matemática, IMPA, 1991.

jogos.tar.gz jogos.ps.gz jogos.pdf view png


Miscellaneous

Reciprocidade quadrática

In portuguese. Eureka!, SBM, No. 15, 27--30 (2002).

recquadr.pdf

O cassino de Cantor

In portuguese. With Carlos Gustavo T. de A. Moreira and George Svetlichny. Matemática Universitária, SBM, No. 28, 67--76 (2000).

cassino.tar.gz cassino.ps.gz cassino.pdf view png

Funções multiplicativas e a função de Möbius

In portuguese. Eureka!, SBM, No. 8, 43--46 (2000).

mobius.ps.gz mobius.pdf

Precisa-se de alguém para ganhar muito dinheiro

In portuguese. Revista del professor de matemáticas, Chile.

otario.tar.gz otario.ps.gz otario.pdf view png

Como perder amigos e enganar pessoas

In portuguese. Eureka!, SBM, No. 1, 41--50 (1998).

bom.tar.gz bom.ps.gz bom.pdf view png

O grupo fundamental e o primeiro grupo de cohomologia de de Rham

In portuguese. Matemática Universitária, SBM, No. 22/23, 14--17 (1997).

derham.tar.gz derham.ps.gz derham.pdf view png

Coordenadas para o icosaedro

In portuguese. Revista do Professor de Matemática, SBM (1996).

icosa.tar.gz icosa.ps.gz icosa.pdf view png

O leão e o homem: perseguição e fuga com posição e velocidade limitadas

In portuguese. With Miriam Abdon and Carlos Gustavo T. de A. Moreira. Matemática Universitária, SBM, No. 17, 22--28 (1994).

fuga.tar.gz fuga.ps.gz fuga.pdf view png

A desigualdade isoperimétrica

In portuguese. With Carlos Gustavo T. de A. Moreira. Matemática Universitária, SBM, No. 15, 13--19 (1993).

dido.tex.gz dido.ps.gz dido.pdf view png

Nomes para ordinais: além da hierarquia de Veblen

In portuguese. O que nos faz pensar, revista do Departamento de Filosofia da PUC-Rio, No. 4, 80--86 (1991).

ord.tar.gz ord.ps.gz ord.pdf view png


Thesis, dissertation

Analytic continuation is impractical

Ph.D. thesis, January 1989, Princeton University.

PhDthesis.pdf

Intervalos errantes e infinitos atratores para funções do intervalo

Dissertação de mestrado, 21 de agosto de 1984, Departamento de Matemática, PUC-Rio (in portuguese).

mestrado.tar.gz


Back to home page